The Rose Bowl Trophy up until 1998, then it became known as the NCAA Division I-A national football championship.
After 1998 the BCS (Bowl Championship Series) rotated to one of six different bowl venues.

Depends on what Bowl it is that particular year. Sometimes its the Rose Bowl or the Orange Bowl, etc.

The NCAA doesn't have a championship trophy. The name of the national championship trophy is the BCS National Championship Trophy.

It's called the "Sears Watercrystal Football Trophy", and it is given to the NCAA champ for college football. It has nothing to do with what bowl game you are in. They give that trophy to the winner of the national championship, no matter what bowl game they played in.

The Sears Trophy

i could possibly be wrong, it has happened before. but i think it's called the ADT bowl championship series trophy. it was called the sears trophy but i think they have changed it with the introduction of the BCS.