Should I choose a new name?

I googled myself the other day. There is a woman with the same name as mine, and she is a published author. It is not a common name at all, but there she is. I’m thinking of either a pseudo, or just a new name. I have no links tying me to the name I have. It seems problematic to me, trying to get into the business with someone else’s name.
Should I?
If yes, then can you offer suggestions?
Funny is okay, but serious is also okay.

To clarify, the name I mean is my real name, not my online name.