Here are the suggestions so far:

Achilles, Adonis, Apollo, Aquilo, Arachne, Ares, Argo, Bailey, Baldur, Bast, Ben, Benjamin, Benny, Bones, Camouflage (Cammie or Camo for short), Captain, Centaur, Cerebus and DeeOGee was our first transport, Champ, Chance, Chip (as in Chocolate Chip or Chip off the old block), Chivez, Clement, Cream, Danny Joe (ie DJ), Elwood, Face, Fritz, Galahad, General, George the Granite Great Dane, GI Joe, Governor, Grande, Granite, Grant, Grub, Guapo, Hamilton, Harely, Harley, Jackson is our alpha cat, Jake is brother-in-laws dog, Jeffery, Loki is in the lead so far, Lucky, Max, Meeko, Mera/Merra, Merlin, Merrka, Milo, Morgan, Moteado (Spanish for Speckled), Mudpie, Murphy, Nelly, Nike, Niobe, Odin, Oliver, Otis, Ozzie, Raiden, Rembrandt (Remmie for short), Ringo, Sampson, Sargent, Shadow, Sombra (Spanish for Shadow), Stoney, Thor, Tiny, Travis, Tristan, Velcro, Winston, Zeus

We haven't picked a name yet, so let us know if you have others to suggest