I don’t think there is really any tax implication from your viewpoint. You’re simply acting as his agent, or potentially a constructive or implied trustee.
If you were to make profit on the transaction then you’d have to declare that profit as income.
If you’re going to keep the bitcoin in your name then you’re effectively holding the bitcoin in trust where he is the beneficiary.
Imagine the situation where an office colleague gives you a fiver for you to get him a cup of coffee - you’re acting as his agent.
If you wanted to get into the details, the areas of law are (1) agency and (2) trust law.
If you or your friend wanted an arrangement that was legally enforceable (you wanted to reserve the right to sue each other) then you might want to get a lawyer to draft an agreement but that is probably overkill if they are a friend that you trust.
These concepts of trust and agency tend to apply only in “Common Law” jurisdictions based on English law (Australia, Canada, New Zealand, US, etc.)