Tom Riddle changed his named from Tom Marvolo Riddle to Lord Voldemort during his Hogwarts years; canon doesn't say exactly which year.
‘Those whom I could persuade to talk told me that Riddle was obsessed with his parentage. This is understandable, of course; he had grown up in an orphanage and naturally wished to know how he came to be there. It seems that he searched in vain for some trace of Tom Riddle Senior on the shields in the trophy room, on the lists of prefects in the old school records, even in the books of wizarding history. Finally he was forced to accept that his father had never set foot in
Hogwarts. I believe that it was then that he dropped the name for ever, assumed the identity of Lord Voldemort, and began his investigations into his previously despised mother’s family – the woman whom, you will remember, he had thought
could not be a witch if she had succumbed to the shameful human weakness of death.'
Half-Blood Prince - page 339 - Bloomsbury - chapter 17, A Sluggish Memory - Albus Dumbledore
Technically, I suppose he would have been between the ages of eleven, when he first learned he was a wizard, and sixteen, when he reveals I am Lord Voldemort to Harry in Chamber of Secrets, via his sixteen-year-old self's memory from the diary Horcrux:
He pulled Harry’s wand from his pocket and began to trace it through the air, writing three shimmering words:
TOM MARVOLO RIDDLE
Then he waved the wand once, and the letters of his name rearranged themselves:
I AM LORD VOLDEMORT
‘You see?’ he whispered. ‘It was a name I was already using at Hogwarts, to my most intimate friends only, of course.'
Chamber of Secrets - page 231 - Bloomsbury - chapter 17, The Heir of Slytherin - Tom Riddle
Canon doesn't indicate that there was any magic involved in the anagram; Tom Riddle uses only letters from the name Merope Gaunt gave to him to create "Lord Voldemort". But note that he doesn't adopt the name "I am Lord Voldemort", which uses all of the letters of his full name. He adopts the name "Lord Voldemort" -- the other letters are left over. So, is "Lord Voldemort" truly an anagram in the purist sense?