How to change my Apple ID for App store to download software

A request for another Apple ID password is often caused by 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. After deleting the apps, it may be necessary to restart the device/computer before you can download the apps again. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID. 

Purchase History Review.  *

Or you can try to set up Family Sharing  between the IDs to keep access to your purchases.

Family Sharing.      

ASC YouTube for Family Sharing   

Family Sharing - Set up.        

Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

You can’t merge multiple Apple ID accounts.

See this Apple article: Change your Apple ID

Change your Apple ID - Apple Support (SG)