It’s up to you. How far do you want to go with it all?
When DJ AM blew up, some felt I should change my name. I didn’t simply because at that point I didn’t dreams anymore of going further than just playing locally on occasion. The only time AM and I crossed paths was when he would come play in Chicago. Even then, locals knew who I was compared to him.
If you’re looking to go big, then you might want to think a rename and rebranding. If you’re just looking to play locally, then I wouldn’t worry about it. You maybe want to use “D2” (imagine the 2 is super scripted) as opposed to “D Squared”.