I wouldn't go with Baxter purely because I live reasonably close to the Baxter detention centre so when I hear it I see bright lights, razor wire and refugees and it gives me the squicks.
Yes! Whenever I hear Baxter, I think of the detention centre too. But I figure if someone has it on their name list, they dont know about Baxter Detention Centre or they aren't concerned about the connotation.
DH suggested it when I was preg with DS1 because we think the NN Bax is cute, but we couldn't get rid of the detention centre connotation, so we didn't use it.