I've had a number of bows with other peoples names on them, and it doesn't bother be at all. When I pick one up to go hunting I just think to myself "come on Mark, (or Fred, or Alex, or Tim), let's go huntin"!" It helps give the bow a little personality.
The first custom bow I had made for me had my name on it. Sold it in a moment of weakness, and then a year or two later bought it back for more than I sold it for. It had passed through a couple different owners in between, and I sure was glad nobody removed my name.