What will happen to purchased apps if I log out of my Google account I'm in the process of moving to a new Google account. Most of the free apps I have, I've already uninstalled and re-installed. However, the purchased apps I'll have to take little by little, because I have some expensive ones, and my budget isn't big enough to do them all at once.

So basically if I log out of the old account, or even delete it, what will happen to the non-free apps? Will they continue to function as long as I do not uninstall them, or will they stop working altogether? I'm assuming I won't receive any updates until I re-purchase them with the new account, I'm fine with that.

I'm eager to delete the old account, but some of the more expensive apps are important to me, so I need to make an educated decision on how to proceed. I'm doing this because I recently changed my surname, and the old Google account is the last remnant of my old name.
When you sign out of the account from which you purchased apps , they will stop working as licencing checks are carried out in the background. Thanks to Izzy who pointed out in comments that this valid only for apps having vending.CHECK_LICENSE active and running. Apparently , all purchased apps don't have this permission running
I have not personally tried this but you may like to give it a shot. Set up a family account . Instructions here. I don't know if you need different billing address / payment method
Another alternative is to add the new Google account to your phone and only use that for mail, Calendar etc. In this case the apps would continue to work but not be updated as explained in Google help