Throughout its storied 46-year history, the on-campus basketball arena at the University of Houston has been named after the late Houston mayor Roy Hofheinz.

Now that the old, out-of-date facility is about to be remodeled, Hofheinz's family doesn't want that to change.

In a petition filed Wednesday in Harris County court, the family urged a judge to block the university from changing the name of Hofheinz Pavilion. UH is currently soliciting donations for a major renovation of the facility. The family says it doesn't want the school to promise a renaming in exchange for a sizable gift.

In fact, the family said in a press release that it believes that such a promise has already been made to a new "anonymous donor." UH didn't address that allegation in a statement Wednesday afternoon. But it did say that it "disagrees with the family's position" about renaming.

According to the family, the building — used for basketball, concerts and special events — was named for Hofheinz after he donated $1.5 million toward its construction in 1969. The arena has been renovated multiple times since then with no name change, the family said. The next renovation will be major, however. University officials have said they are hoping to raise $25 million for the work.

But taking Hofheinz's name off the facility to pay for that update would be wrong, a lawyer for the family said. Hofheinz, who died in 1982, served in the Texas Legislature, served as Harris County judge and was mayor for two years. His family said he fought to desegregate city hall, pushed for major transportation initiatives in Houston and was involved in bringing what would become the Houston Astros baseball team to town.

But the family said in a press release that "Hofheinz Pavilion is the only public structure in Houston bearing his name." And taking his name down would break a promise made when the stadium was built.

"There was only one condition on the donation: for once, something in Houston that he helped build would bear his name," John Raley, an attorney representing the family, said in a press release. "The University agreed, took his money, spent it, and now wants to break their agreement. That is illegal and, as any fair minded Texan can see, simply wrong.”

The university said it disagrees but it is trying to find an amicable solution.

"The University of Houston appreciates and celebrates the generosity of all its donors and complies with the donors’ intent and restrictions set forth in gift agreements," it said in a statement.

Disclosure: The University of Houston has been a financial supporter of The Texas Tribune. A complete list of Tribune donors and sponsors can be viewed here.