Ok, figured it out. In honor of the greatest running back in NFL history's last season, I'm going to go with the 1987 Chicago Bears. Since the Bears used to play in Wrigley Field, that's what I will use as my team's ballpark.
Starting pitchers:
Walter Johnson ----- Will Johnson, DE
Mordecai Brown ----- Kevin Brown, P
Frank Smith ---------- Sean Smith, DE
Relief Pitchers:
Mariano Rivera ------- Ron Rivera, LB
Jim Brewer ------------ Chris Brewer, RB
Don McMahon -------- Jim (Headband) McMahon, QB
Greg McMichael ------ Steve (Mongo) McMichael, DL
Bill Harris --------------- Chuck Harris, OL
Grant Jackson --------- Vestee Jackson, DB
Billy Wagner ----------- Bryan Wagner, P
Catchers:
Walter Blair ------------- Paul Blair, OL
Gene Oliver ------------ Jack Oliver, OL
Infield:
Frank Thomas --------- Calvin Thomas, RB
Tony Phillips ------------ Reggie Phillips, DB
Buddy Bell --------------- Bobby Bell, LB
Jay Bell ------------------- Todd Bell, DB
Gregg Jefferies --------- Eric Jeffries, DB
Heinz Becker ------------ Kurt Becker, OL
Brendan Harris --------- Al Harris, DL
Outfield:
Joe Jackson ------------ Leonard Jackson, LB
Hack Wilson ------------ Otis Wilson, LB
Brady Anderson ------- Neal Anderson, RB
Jay Payton -------------- Walter (Sweetness) Payton, RB (it is his tribute after all)
Craig Gentry ------------ Dennis Gentry, RB
And last but not least, since it's a baseball team named after football players, I had to include someone that played both!
Deion (Prime Time) Sanders ---- Thomas Sanders, RB