Q: Serial number linked to another Apple ID (not mine)

Please visit this page and enter the serial number:

https://www.icloud.com/activationlock/

You said "... Brand new, unopened ..."  If the check from the above website displays "Activation Lock: On", then the eBay seller did a nice job of repackaging what is likely a stolen iPhone.

If your iPhone is Activation Locked, you will never be able to use it without contacting the original owner.

Find My iPhone Activation Lock - Apple Support

He likely used store pickup or purchase in an apple store and his id was linked.

You should be fine using the phone without issue.  Just anytime you go to an Apple Store or call for help that persons name will come up.

The only way to free up the support profile is if the seller removes it from theres.

Excellent.  Enjoy your iPhone.