Daemon Waters was a bastard son of King Aegon IV Targaryen, so when he was legitimized, he should have taken the name Targaryen (and be one of the latest siblings) correct? Like Ramsay Snow who took the name of his father, Bolton.
After readig this question - Benefits of joining The Night's Watch - I think that as he is not the oldest boy of his siblings and a bastard, why didn't he have a lower career like a member of the Night's Watch?
Well first of all, this is a very intriguing question which has bugged me a lot personally.
Daemon was a bastard but he was a Targaryen on both sides, having Aegon IV as his father and Princess Daena the defiant as his mother. So that makes it all the more interesting. Why chose the new name? It must be noted that Daena was heir of her brother King Baelor but her claim was ruled out by Lords of the realm who made her uncle Prince Viserys the King. If it had been Daena who was crowned instead of Viserys, Daemon would have been first in line to throne after getting legitimized by his mother.
He was however, not the eldest born son of the King, natural or legitimate. Daeron II was the eldest and legitimate child of Aegon IV.
King Aegon however suspected that Daeron was not his son at all. He had always known that his sister-wife Naerys and his brother Aemon (The Dragonknight) were too close to each other. Even when Aegon and Naerys wed, Aemon had a physical brawl with Aegon.
She loved Aemon best of her brothers, for he knew how to make her laugh—and he had something of the same piety that she possessed, while Aegon did not. She loved the Seven as dearly as she loved her brother, if not more so, and might have been a septa if her lord father had allowed it. But he did not, and Viserys instead wed her to his son Aegon in 153 AC, with King Aegon III's blessing. The singers say that Aemon and Naerys both wept during the ceremony, though the histories tell us Aemon quarreled with Aegon at the wedding feast, and that Naerys wept during the bedding rather than the wedding.
The World of Ice and Fire: Targaryen Kings-Viserys II
The resentment only grew when Aegon started torturing Naerys and humiliating Aemon as his revenge.
Matters between them were inflamed further by Prince Aemon, their brother, who had been inseparable from Naerys when they were young. Aegon's resentment of his noble, celebrated brother was plain to all, for the king delighted in slighting Aemon and Naerys both at every turn. Even after the Dragonknight died in his defense, and Queen Naerys perished in childbed the year after, Aegon IV did little to honor their memory.
The World of Ice and Fire: Targaryen Kings-Aegon IV
Given his petty nature, he bestowed the ancestral Targaryen sword on Daemon instead of Daeron. Some people, like Prince Maekar, Argued that it was only because Daemon was a puissant warrior while Daeron had a bookish non-martial nature.
"My father (then-Prince-and-later-King Maekar) says that was because Daemon was a swordsman, and Daeron never was," said Egg (then-Prince-and-later-King Aegon V). "Why give a horse to a man who cannot ride? The sword was not the kingdom, he says."
The Sworn Sword
Later on, he started suspecting that Daeron was actually a bastard of Naerys and Aemon.
The king's quarrels with his close kin became all the worse after his son Daeron grew old enough to voice his opinions. Kaeth's Lives of Four Kings makes it plain that the false accusations of the queen's adultery made by Ser Morgil Hastwyck were instigated by the king himself, though at the time Aegon denied it. These claims were disproved by Ser Morgil's death in a trial by combat against the Dragonknight. That these accusations came at the same time as Aegon and Prince Daeron were quarreling over the king's plans to launch an unprovoked war against Dorne was surely no coincidence. It was also the first (but not the last) time that Aegon threatened to name one of his bastards as his heir instead of Daeron. After the deaths of his siblings, the king began to make barely veiled references to his son's alleged illegitimacy—something he dared only because the Dragonknight was dead. His courtiers and hangers-on aped the king, and this calumny spread.
The World of Ice and Fire: Targaryen Kings-Aegon IV
As King Aegon allegedly wanted to remove Daeron as his successor and name Daemon instead, Daemon was not sent to the Night's Watch. Aegon however never actually took any steps in this regard given the marital alliance Daeron had with the Dornish and popularity of the Prince among many lords.
Younger Targaryens have never taken the black in history except Maester Aemon1. They usually:
It must be noted that Daemon had adopted the name Blackfyre before his actual legitimization.
Daemon was the name Daena gave to this child, for Prince Daemon had been the wonder and the terror of his age, and in later days that was seen as a warning of what the boy would become. Daemon Waters was his full name when he was born in 170 AC. At that time, Daena refused to name the father, but even then Aegon's involvement was suspected. Raised at the Red Keep, this handsome youth was given the instruction of the wisest maesters and the best masters-at-arms at court, including Ser Quentyn Ball, the fiery knight called Fireball. He loved nothing better than deeds of arms and excelled at them, and many saw in him a warrior who would one day be another Dragonknight. King Aegon knighted Daemon in his twelfth year when he won a squires' tourney (thereby making him the youngest knight ever made in the time of the Targaryens, surpassing Maegor I) and shocked his court, kin, and council by bestowing upon him the sword of Aegon the Conqueror, Blackfyre, as well as lands and other honors. Daemon took the name Blackfyre thereafter.
The World of Ice and Fire
Notice, Daemon is granted Lands at 12 in 182 AC (Given that he was born in 170 AC) by his father and takes the name Blackfyre. He was not legitimized back then therefore legally not allowed to use the name Targaryen, so that way he founded a bastard Cadet dynasty.
Aegon IV died in 184 AC, that's when he legitimized his children including Daemon. So Daemon wasn't a legal member of House Targaryen for two years while he had his own dynasty and name. Afterwards, he never gave up his own dynasty name in favor of Targaryen name.
He decided to found a cadet dynasty of House Targaryen, fully aware that he or his descendants were not in the line of succession given that Daeron was young and later went on to have sons and grandsons of his own.
This is not unheard of. We have seen how even the legitimate younger sons of noble houses have founded cadet dynasties. E.g. The Karstarks and Greystarks are cadet dynasties of House Starks, founded by younger legitimate sons.
The Karstarks traced their descent to Karlon Stark, a younger son of Winterfell who had put down a rebel lord a thousand years ago, and been granted lands for his valor. The castle he built had been named Karl's Hold, but that soon became Karhold, and over the centuries the Karhold Starks had become Karstarks.
A Storm of Swords: Catelyn III
Also
Ser Bartimus had no interest in the world outside, or indeed anything that had happened since he lost his leg to a riderless horse and a maester's saw. He had come to love the Wolf's Den, however, and liked nothing more than to talk about its long and bloody history. The Den was much older than White Harbor, the knight told Davos. It had been raised by King Jon Stark to defend the mouth of the White Knife against raiders from the sea. Many a younger son of the King in the North had made his seat there, many a brother, many an uncle, many a cousin. Some passed the castle to their own sons and grandsons, and offshoot branches of House Stark had arisen; the Greystarks had lasted the longest, holding the Wolf's Den for five centuries, until they presumed to join the Dreadfort in rebellion against the Starks of Winterfell.
A Dance with Dragons: Davos IV
So if even Legitimate aristocrats can found their own dynasties separate from the parent sense, it should not be very shocking that a bastard decided to do the same.
Not to mention, Daemon had to do it anyways because he held lands from his father despite being a bastard and a Lord needs a dynasty name.
Daemon was by all accounts a proud man. Being founder of a Dynasty is something that would attract that kind of man when the alternative was being a younger and minor member of a centuries old dynasty.
That also made him unique among his other siblings and set him apart from others while boasting of the pride that they held the sword.
There have to be some political motives as well. People knew that Daemon wielded the sword of the Targaryen Kings. If Daemon had taken the Targaryen name, he would have just been a younger Targaryen wielding an ancestral sword like his half-brother, Brynden Bloodraven wielded Queen Visenya's sword, the Darksister.
By choosing the name Blackfyre, he emphasized the fact it was him who bore the sword of the Kings in mind of anyone who heard that name. In this way he separated himself from both Brynden and Daeron, putting himself on the political map as a possible claimant to the throne. He reminded everyone by using that name that it was he who held his father's favor and he who wields the conqueror's sword.
However it must be noted that Daemon did not want to be the King initially. It is said that it was his half brother Aegor mainly along with other dissident lords who changed his mind.
In conclusion, It is clear that:
1. Aemon did not initially join the NW either. He joined the Citadel. He only went to NW out of his own accord to avoid being used against his brother Aegon
The name of House Blackfyre was taken from the Targaryen sword Blackfyre. King Aegon IV gave his bastard son Daemon Waters instead of his heir, Daeron, later Daeron II. He legitimatized all of his bastards on his deathbed, and many of them rebelled. This was known as the Blackfyre rebellion, and the biggest usurper was Daemon Blackfyre. Many saw him as king, since he held the sword that had been Aegon the Conquerer's, and so he created House Blackfyre, calling himself King Daemon I Blackfyre.
For more, here's the wiki page.
For even more info on Daemon's life, see Aegon's answer down there.
