So.... shouldn't IRS have changed the database by now ?   

Oh, you're so rhetorical...  I would bet in your younger days, you were romantic too....

Never been in this situation, but the imaginative part in me came up with a few thoughts, mostly based on Murphy's law and my less-than-cluelessness on how IRS is functioning these days..:

1.  The extension was taken in the old name.  I would send a paper extension under the new name, with a short letter referring to the name change and a statement that efiled extension was accepted in the old name and it's a duplicate.  In case the processing of the e-extension was messed up, due to it being in the old name, the extension would be "preserved" by the paper filed one.  Just because Lacerte (or TT or PS or whatever initials your software goes by) says it was accepted does meant squat.  I'm still pacifying my client in fighting a 2020 S Corp late filing penalty that Lacerte shows "efile accepted".  Also there is a slight chance (only ironman could give us a precise %) that someone processing that extension would look into the name change and actually effect the name change.

2.  On April 29, after returning from Hawaii, I would call the IRS Petitioners Hotline to see if it's still operating and if so whether folks there could help.

3.  The extended due date is September, a few months down the road.  I would suggest to client to file right before the extended due date.  Perhaps magic happened and your rhetorical question is answered by then.

4. I would try the efiling first with the new name.  The facts are on the client's side.  If accepted, keep fingers crossed.  If rejected, fall back on plan B (or is it A for you?) that is: Old name with "name change" marked.  In this case, plan to repeat all the steps in March 2023 for the 2022 filing..  The rhetorical question is optional.

Sorry I can't give you very definitive suggestions, except perhaps sign on the iRS website and type and send "I need to talk to someone" like a thread here over the weekend and see if it works..

Just a few random thoughts before changing the clocks on the office walls and OMG, it's past 9 am already....  Thought it was eight something....Got to go......