go under the name of (something)
To use the specific name (that is then stated). My daughter Margaret has now decided that she goes under the name of Calliope. I'm looking for a man who goes under the name of Whitaker. Do you know him?
go under the name of something
[for someone or something] to be known under a particular name. Now she goes under the name of Suzanne. The man you just met goes under the name of Walter Sampson.