http://www.baseball-reference.com/a/arftha01.shtml
Here's another first baseman: Henry "Bow Wow" Arft.

And if you're really hard up for an outfielder, there's always Glen Barker.

Oops, sorry for the funky HTML code. Someone please delete the previous comment ... here it is correctly.

Somebody seems to have appropriated "Hall of Names" ... oh, wait, Craig outranks me and is a member of the Cabal (there is no Cabal), so I guess that's acceptable.

George "Doggie" Miller was mostly a catcher, but played more than 300 games in the outfield.

Mutt Williams and Mutt Wilson were both pitchers.

Maybe you could use all-time Mr. Marlin, Jeff Canine ...?

Wasn't Eric Davis sometimes called the E-Dog?

Rickey Henderson has often been accused of being a Hot Dog. Does that count?

We'll go with Doggie Miller.

Now let's do birds! Start with Ron "The Penguin" Cey at third, Tris "The Gray Eagle" Speaker and George "The Stork" Theodore in the outfield, Mark "The Bird" Fidrych on the mound...

Turkey Stearns, Chicken Wolf, Jake "Eagle Eye" Beckley...

Not really a name, but the first thing that comes to mind is Dave Winfield and the 'Seagull Incident'.

Andre "The Hawk" Dawson, Phil "The Vulture" Regan. I don't suppose the Flying Dutchman counts as a bird.

Uh ... how about former pitcher Doug Bird?

The Flying Dutchman was a ghost ship.

Maybe Pete Falcone?

Your manager is Ivey WINGo. The umpire is NESTor Chylak. George CROWE was an All-Star outfielder.

and of course Paul and Marlon Byrd and manager Birdie Tebbetts.

Ooh! Ooh! Hall of Famer Joe "Ducky" Medwick! Former "next Tom Seaver" Met pitcher Craig Swan! The greatest Atlanta Brave of all time, Ralph "Roadrunner" Garr!

Ohhhh yeah.

I like "bulldog" for Josh Towers. He is Hershiserian on the mound, with a bit more edge. The ironic thing: Towers is terrified of dogs, he was bitten as a young boy.

Rick "Rooster" Burleson for shortstop.

Jays qualifiers:

Jeff Byrd, Goose Gozzo, (goose gossage), Pedro Swann,

Or how about... Brandon Duckworth.

Jimmie Foxx (who's usually being chased around by Torii Hunter)

Some pitchers to ruminate upon:
Joe Wolf
Joe Gibbon
Ted Lyons (close enough)
Robin Roberts
Jack Russell (Terrier)

Hey Dogz! Woof, woof ... Da Birdz would sweep you in four (note several newcomers to the above suggestions and the fact that we did not fall back on the fact that there is a bird called the "martin," a common first AND surname):

C/MGR Birdie Tebbetts***
1B Nelson "Chicken" Hawks
2B Marlon Byrd
SS Rick "Rooster" Burleson
SS Fred "Chicken" Stanley
3B Ron "The Penguin" Cey
OF Tris "The Grey Eagle" Speaker***
OF George "The Stork" Theodore
OF Turkey Stearnes***
OF Andre "The Hawk" Dawson
OF George Crowe
OF Joe "Ducky" Medwick***
OF Ralph "Roadrunner" Garr
OF Leon "Goose" Goslin***
OF Ken "Hawk" Harrelson
OF Jose Cardenal
OF Pedro Swann
SP Robin Roberts
SP Mark "The Bird" Fidrych
SP Paul Byrd
SP Craig Swan
SP Brandon Duckworth
SP Mike Parrott
SP/RP Doug Bird
SP/RP Joel Finch
RP Rich "Goose" Gossage
RP Phil "The Vulture" Regan
RP Mauro "Goose" Gozzo
RP Ducky Swan (one game, one inning in 1914 ... but the name!)
MOP Jeff Byrd (sorry Jays fans, he was 2-13 in his only year)
UTIL Jimmy "Chicken" Wolf
COACH Ivey Wingo
UMP Nestor Chylak***

*** Indicated Hall of Fame

Note, Robin Roberts*** ... also in the Hall of Fame. Missed that one.

Any creative teams with fruit in honor of my man Mark Lemongello would surely win any competition... :)

Lemongello made the very first-ever Hall of Names team ... the All-Food Team.

If you're going to do the "All Bird" team or the "All Dog" team, ya gotta toss in a cat, just to mix it up a bit.....How about Frank "Cat" Catalanotto???

Seeing as this thread has popped out of nowhere, it occurs to me that Negro League great shortstop Dobie "Black Cat" Moore qualifies for both the cat and the dog team.  I guess that he was "bi-special".