Two Apple ID’s on same MAC, and the purchase of a new iPhone 14

I have a Mac, of course I wasn’t smart enough to just get a laptop, and when we purchased we put it under my wife’s name. I guess that generated an Apple ID for her when we established an iCloud account. Then, I decided for some strange reason to get my own iCloud account, which is under a different Apple ID. Oddly enough I don’t think I have ever even used my account.

NOW, I just purchased an iPhone 14. My Samsung almost caught my pants on fire. I can’t get the bluetooth to pair with my MAC. If I connect it with the cord the Mac shows it on my devices connected. I can sometimes get the iPhone to show up on the Mac’s bluetooth devices. There is a “connect” button on the Mac’s bluetooth screen. When I hit it, it disappears from the screen. On my iPhone, it says that I cannot connect or it isn’t recognized.

After sometime on the chat line, they said that the two different Apple ID’s are not allowing me to pair the iPhone to the MAC.

SO, here’s the question. If I delete my Apple ID on the MAC, can I edit my wife’s Apple ID with my name, so it will pair up?

Sorry if this doesn’t make sense.