Newt’s names all seem to refer to his connection with animals.
Most obviously, a newt is a type of amphibious creature that looks like a lizard. Newts are also commonly associated with witchcraft, as ‘eye of newt’ is an often-used potion ingredient. His full first name, Newton, means ‘from the new town’, which has no clear connection to Newt himself.
From a surname which was originally derived from a place name meaning "new town" in Old English. A famous bearer of the surname was the English physicist Isaac Newton (1643-1727).
- Given name Newton (Behind the Name)
However, it seems most likely that Newt got his first name because of the animal - J.K. Rowling has used names that are obviously connected in a clear and simple way with the character’s ‘specific skill’ or chosen field of work before, like Sprout being the Herbology professor and Vector being the Arithmancy professor, especially with more minor characters.
Artemis is most commonly known as the Greek goddess of the hunt, but she’s also the goddess of wild animals and the wilderness, most likely referring to Newt’s love of animals and the wilderness.
Artemis, in Greek religion, the goddess of wild animals, the hunt, and vegetation, and of chastity and childbirth; she was identified by the Romans with Diana.
- Artemis (Encyclopedia Britannica)
This name is most likely chosen after the Greek goddess, as being the goddess of the wilderness and animals, she’s associated with the same sort of things as Newt would be as a Magizoologist.
While the meaning of the name Fido is ‘I am faithful’, it’s most commonly associated with being a name for pet dogs, and the name is basically a shorthand for ‘pet dog’.
Means "I am faithful" in Latin. This name is commonly given to dogs.
- Fido (Behind the Name)
It seems likely it was chosen because of the name’s strong association with an animal.
Several sources indicate that ‘Scamander’ is an archaic word used to mean ‘to wander around with no settled purpose’, which would relate to Newt’s many journeys studying animals. Given its clear connection to Newt, and considering JKR’s fondness of using old words as character names (like Dumbledore meaning bumblebee), this seems to be the most likely origin of Newt’s last name.
Scamander, to wander about without a settled purpose;—possibly in allusion to the winding course of the Homeric river of that name.
- The Slang Dictionary: Etymological, Historical, and Anecdotal
‘Scamander’ is also the name of a relatively minor Greek god, as well as the river associated with him, which may also be where the word ‘scamander’ derived from. Newt’s middle name Artemis and his brother’s name Theseus are also rooted in Greek mythology. However, despite that, there’s no clear reason why Newt’s last name would be chosen as a reference to this river god specifically, other than the word possibly based on his name - nothing clearly connects anything about Newt to the god Scamander or the legends surrounding him (besides its use as a term meaning to wander).
Scamander was a Greek river god, a Potamoi, and therefore one of the 3000 sons of the Titans Oceanus and Tethys, and therefore Scamander was a brother of the 3000 Oceanids, the water nymphs. Each river in the ancient world would have a Potamoi associated with it, and this river god would live and die with the life of the river.
Scamander was therefore the Potamoi of the Scamander River, a river now known as Karamenderes, but this Potamoi was also known by the gods as Xanthos, and therefore gave his name to the Lycian city.
- The River God Scamander (Greek Legends And Myths)
‘Scamander’ also sounds like ‘salamander’, which is the family of amphibians that newts are classified as. So newts are part of the salamander family, and Newt is part of the Scamander family.
Newts are members of the Salamandridae family, and there are over 60 species. All newts are salamanders, but not all salamanders are newts. The differences between newts and salamanders are few, according to Caudata Culture, a website for newt and salamander enthusiasts.
- Facts About Newts (LiveScience)
This may or may not be intentional, but it’s certainly an amusing coincidence, if nothing else.