A future name change for Lamar University and the other three Lamar-named schools always is a possibility. I've heard some of that talk, and the "Texas State University-Beaumont" name is the most often discussed rumor. However, schools like Sam Houston, which has a long and storied history, would resist such a change.
Just a note to WO795: Lamar State College-Port Arthur and Lamar State College-Orange did not "break away" from Lamar University. They were independent schools which just happened to belong for a period of time to the LU System. When the system was abolished, they were added to the Texas State University System, where they remain as independent schools.
Lamar State College-PA was founded in 1909 as Port Arthur College, long before there was any thought of Lamar University.