In theory it doesn't matter since AppleCare is for the device itself, not the user. However, it may be more convenient for it to be done under the name of the person who may have to do the work should you need to use the policy. That's probably going to be you.
To note:
Transfer your AppleCare plan - Apple Support - https://support.apple.com/HT202712
Transfer your AppleCare plan to a new owner
1. Sign in to My Support (https://support.apple.com/en-in/my-support) to get the AppleCare agreement number, the serial number of the device, and the proof of coverage for the AppleCare plan.
2. Find the original sales receipt for the device.
3. Get the new owner’s name, address, email address, and phone number.
4. Contact Apple Support. https://getsupport.apple.com/?caller=kbase&PGF=PGF66001&category_id=SC0089&symptom_id=20455
Edit: I suspect you also bought the device so likely the receipt has your name on it and therefore it would be easier for you to purchase AppleCare. However, do please read the entire transfer document since there are several critical restrictions.