Another vote for the best first name, ideally the first one in the passport, and the patronymic name, ideally the last in the passport, and don't overdo it. BA aren't that fussy about this, though there is always a risk an awkward agent may cause problems, If there is an identity card that backs this up, just in case, even better. But there is no requirement to get the full passport name into the booking. In fact the first name can be just a single letter abbreviation.