Is this a new computer?
If the applications that need updating are Apple applications that came with the computer, try going to the App Store Purchases tab or click on your profile and then go to Purchases to see if there is an option to accept the applications with your Apple ID. If that doesn't work, you can delete the applications and download them with your Apple ID. The applications are free. You may have to sign out of the App Store, restart the computer, and sign back in to download new copies.
Purchase History Review
If it isn't a new computer, a request for another Apple ID password is often caused by updates to apps/purchases that were made when using the other ID. Those purchases are tied to the other ID and can't be transferred. One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID.
Purchase History Review.