Complex sentence: Computer technology firm Compaq bought naming rights to the building after that and it was known as Compaq Center until 2003, when the Toyota Center replaced it as a new professional sports venue in Houston.
Split into simpler sentences: Computer technology firm Compaq bought naming rights to the building after that and it was known as Compaq Center until 2003. At that point the name was dropped, coinciding with opening of the Toyota Center as a new professional sports venue in Houston.