Gifting an Apple Watch with monthly installment

I bought an Apple Watch through installment plans in order to gift it to a family member for their birthday, and I was wondering if the person receiving it is able to pair it with their own phone number since it gave me an additional line with already a phone number there. And if it won’t lock if they end up changing SIMs card or something since I’m still paying it off. I’m able to pay off the watch next two months but wondering if there’s a way I can still make the monthly payment on my account and not transfer over to theirs.