To reassure you, you'll still be covered by the warranty even if the product isn't registered.
Any more info on which bit of the registration isn't working for you? E.g. are you doing it through the Members app or a web browser (if it's a browser, which one, and have you tried another to see if it works on that)? Which step isn't working? Any error messages you're getting at that point?
There's more info on registering Samsung products here: https://www.samsung.com/uk/support/mobile-devices/register-samsung-product/ (although these days registering through the Members app is through Support > + Register).