how can i switch over apple care

"...switch over apple care..." to what? What are you trying to do?

For each Mac, you can only purchase Apple care once. It protects you out to 3 years from date of purchase. You can not extend it beyond that. You can not transfer Apple care from one Mac to another.

When you receive a Macbook Pro as a gift. If it is new or refurbished, it comes with one year of apple care. that can be extended to three as long as it is done before the one year expires. If, when purchased, the apple care was not put in your name. The person who bought it is the one that can, through apple, transfer it to you.

IME the "who" on the Applecare agreement isn't critical. The Applecare sticks with the Mac's serial number regardless of who owns the Mac.

Here is what apple says. https://support.apple.com/en-us/HT202712

That's not what apple says. click the link I just posted.

The information in the article indicates that you "can" but does not indicate that you "must". If you notice, the check coverage site (https://checkcoverage.apple.com/) only needs the device's serial number.

I don't know. This came up when my daughter sold her Imac, which had 3 years of apple care. We asked about it at the genuis bar. They said that the apple care did not automatically go along if she sold it,. But she could transfer it. That was what I was going by.

It's best to transfer it when you can.