Obviously this is a personal preference, but I would say no.
It really does not matter. Just choose the name describe your schnauzer.
Skippy Baxter's birth name is Lloyd Baxter.
Baxter Ward's birth name is Baxter Ward Schwellenbach.
Biddy Baxter's birth name is Joan Maureen Baxter.
Clifton Baxter's birth name is Clifton Keith Baxter.
Crysten Baxter's birth name is Crysten Unique Baxter.
Leeds Baxter's birth name is Leeds Lincoln Baxter.
Lonny Baxter's birth name is Lonny Leroy Baxter.
Meredith Baxter's birth name is Baxter, Meredith Ann.
Warner Baxter's birth name is Baxter, Warner Leroy.
The breed of dog you are referring to is spelled "Schnauzer."
Artie Baxter's birth name is Arthur Kenneth Baxter III.