The purpose of a false identity is to blend in or obscure. What logical reason would there be to use a false name for the entirety of my stay? No one from my world is here. I did not know other worlds knew of me until I met a man who both was and wasn't my own brother. Only after that did I learn that Sherlock Holmes was also a famous fictional character.

The fact that I cannot match anyone's expectations of Sherlock Holmes puts more attention upon me. It obscures nothing. There is no reason to continue using that name unless it was truly mine.

[ He doesn't even know exactly what his username references. Is it his mother? The flower? The color? He can guess that perhaps "a study in violet" could refer to how he learned the truth about his mother on Cordona, but that still suggests nothing to him about a great detective. ]