I've done a quick search but haven't found any convincing answers for a couple of situations, which I will be facing.
1) The person's byname is 'X alias Y' for their entire lives. It may occasionally be recorded as 'Y aias X'. This is a situation where a family as a whole may well have become known in this fashion for a generation or two. THey were baptised and buried as 'X alias Y' and did not acquire the alias themselves.
2) A person in mid-life known as 'X alias Y'. They may fit category 1, but I don't know that, or which name was their birth surname if the alias was acquired during their lives.
Edit: This is in an English context, 16th and 17th centuries.