They’ll be regnants, surely, not regents? Unless I’ve got it completely wrong, a regent is someone who stands in for the monarch, e.g. if they’re underage.
Yup, yup, you are right they will be Queen XXXX, R. = Regnant
That's not what the R stands for --it's Regina. QEQM of the UK signed her name Elizabeth R, as did Queen Mary, her mother-in-law. For men, the R stands for Rex. Edward VIII used P when he was prince of Wales (Princeps).