A little bit of trivia: In French, the word "vol" means "flight" or "robbery". "Mort" is "death" in French. If we put the two together, "Vol(de)mort", it means "flight from death" or "escape from death," which is what Voldemort's entire philosophy was: to not die, to live forever, to become immortal. According to J.K. Rowling, the "t" at the end of "Voldemort" was intended to be silent, but nobody else pronounces it that way.
In regards to the actual name itself, translations aside, it's correct that Tom Marvolo Riddle hated going by his father's surname. He hated the fact that a wretched Muggle was related by blood to him. In order to disguise this, he essentially demolished the name by scrambling the letters and coming up with "I am Lord Voldemort," a title which he took up during his school years, once he gathered a following of like-minded allies. He never had any true "friends," just people who feared and followed him and shared the same ideas that he did. He did this to try to shred any connection to the Muggle Riddle, and then finished it off by killing his father (albeit not entirely for that one reason).