Blended and merged names need a deed poll
A blended name, sometimes called a meshed name, takes letters from both surnames to make a new one. It isn’t a double-barrel, so your marriage certificate doesn’t explain it. A deed poll does: it records your old name, your new name and your declaration that you’ve adopted the new one for all purposes.
Each person changing their name needs their own deed poll. If you’re both becoming Tayloss, that’s two deed polls, each signed in front of two witnesses. You can sign them on the same day with the same two witnesses, as long as neither of you witnesses the other’s.