Thanks to Mac and others for the response. Yep, Abdim works just fine for BIAB, and as you say the G on top is just the melody note. I just didn't know if there might be a simpler name for the chord including the G. Probably not.

Mac, there are probably a couple of guitar teachers turning in their graves, but I couldn't play without the old thumbover. That one is simple. Hey, I could have tried it with Db9b5, played like this, with thumb wrapped over to the 5th string: X43443. I can barely pull that one off, and certainly couldn't if my fingers were the least bit fatter!

Bill R