Someday AFH will be upgraded (replaced? Nah) AND renamed...

... because in all likelihood Self is going to win at least another NC, and if he stays long enough he will pass Phog as the winningest coach in KU history, and there really is nothing of significance left to name after him when he steps down.

So what do you think of this -- The Allen-Self Center

Hmmm, better make that The Allen-Self Arena or maybe better yet keep it simple --
Allen-Self Fieldhouse
(although technically the ol' barn hasn't been a fieldhouse in decades, but let's take a stand for lineage and tradition!).

With a statue of Bill to complement the statue of Phog, of course.

Hmmm, maybe the pun possibilities would be worth the first name?

Nah, I can't see the KU admin going for it.

Shoot, they wouldn't even pitch in to help get The Rules home, why should we think that their successors will be any less anal retentive?

Note well -- either way, as long as Allen is in the name, it will be called The Phog.

And (imagine Andy Rooney voice here) don't you just hate springing forward every year?

When it comes to KU hoops I'm a rather staunch traditionalist, so I'd say keep it Allen Fieldhouse for at least a decade after Self has departed. Give it all time to marinate, if you will. And if he's both surpassed Allen and brought home another NC or three (heehee, you saw what I did there), then I'd opt for Allen-Self Fieldhouse. NOT Allen-Self Arena. Yuck! Sounds like the DeanDome, or TTSDome in HE's vernacular.

PS: Yes, once The Phog, always The Phog...