Least unique name:

Tigers - 5 schools (Aubrun, Clemson, LSU, Memphis, Missouri)

Nicknames with 4 schools:

Bulldogs - (Fresno St, Georgia, Louisiana Tech, Mississippi St)

Wildcats - (Arizona, Kansas St, Kentucky, Northwestern)

Nicknames with 3 schools:

Aggies - (New Mexico St, Texas A&M, Utah St)

Cardinals - (Ball St, Louisville, Stanford - yes I know it's Cardinal, but it's close enough to count)

Cougars - (BYU-Provo, Houston, Washington St)

Eagles - (Boston College, Eastern Michigan, Southern Mississippi)

Huskies - (Connecticut, Northern Illinois, Washington)

Owls - (Florida Atlantic, Rice, Temple)

Nicknames with 2 schools:

Bears  - (Baylor, Cal)

Broncos - (Boise St, Western Michigan)

Bulls - (Buffalo, Southern Florida)

Cowboys - (Oklahoma St, Wyoming)

Falcons - (Air Force, Bowling Green)

Hurricanes - (Miami, Tulsa)

Knights - (Army, Central Florida)

Panthers - (Florida Atlantic, Pittsburgh)

Raiders - (Middle Tennessee, Texas Tech)

Rebels - (Mississippi, UNLV)

Spartans - (Michigan St, San Jose St)

Trojans - (USC, Troy)

Wolfpack - (NC St, Nevada)

And, of course, team names derived from Indian tribe names:

Aztecs (San Diego State)
Chippewas (Central Michigan)
Illini (Illinois)
Indians (Arkansas St)
Seminoles (FSU)
Utes (Utah)