Buy As Gift:

My friend is not on the list

Whoever you have chosen here at the moment when payment is received and VIP is delivered in-game is the person who will receive it, so you must make sure that it is set correctly at that moment.

If your friend is not on the list at all it is because they have never signed in to and so we do not have their account details. Get your friend to sign in through Steam one time and you will then be able to find them on the list.

They may also be listed with an old Steam username. Get them to ReSync Steam Account Details from Account page to update their list name to their current Steam username.