Thats what I do. Unless the player I buy is a scout then I change the name since I'm 'first owner' lol
I once had a player named Yossi Benayoun. Also currently have David Rocastle and Robbie Savage at my club.
I have decided that from every season I will name a player after a Arsenal Legend, Savage being the exception, since he is everywhere these days as a sport pundit and you can't get of him, but Savage is great because he can be a bit of a trouble maker and wind-up merchant like in real life lol.