Baxter definitely fits with the others better ...
But it's a dog name to me; I've known two people, within the last year or so, with dogs named Baxter. Both bulldogs.
It's Ber-Nard. I think that's how most people would say it.
Barney is definitely a dog's name, or an obnoxious purple dinosaur. Barnaby and Barnabas are just too cartoonish,and Bernard is ugly.
I think, therefore I judge.