new iPad asking for password for an 'apple ID' that I didn't know I had

It doesn't sound to me like the iPad is a "new" as you make out. It may be new to you but it had a previous owner who should have done the things in this article: What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

If it is an app asking for an ID to be updated, the only way I know of to identify which one it is needs to be done by turning off automatic updates and then update each app manually as new updates appear. When you find one that fusses then you know that one at least needs to be deleted.

Ideally though, you should prepare the device as if you were selling it. There may be worse surprises in store for you if it was not wiped properly before you bought it.

Take it back to the store. A truly new iPad should not be asking for any Apple ID in particular. It should only be inviting you to sign in with one. Whichever one you want to use.

Even if you find an app that needs deleting, you may find that ultimately you are locked out completely from the device. That is why you need to take it back and get a refund or have it reset properly.