It is forbidden on Shabbos to give a Matono, a gift. This is a form of a Kinyan, an acquisition, and there is a transfer of ownership from one individual to another. As it is forbidden to make a Kinyan or perform an acquisition on Shabbos, gifts are forbidden to be given on Shabbos.
One is allowed to give gifts if they are Minei Maachal Umashke, food and drink which is needed for Shabbos. Even utensils used for the Shabbos meal are permitted to be given as a gift on Shabbos. However, clothing and other such items should not be given as a gift on Shabbos.
Giving a gift to a Bar Mitzvah boy would obviously be a problem based on this, unless it is food or drink. An option in order to be able to give a gift to a Bar Mitzvah boy on Shabbos is to arrange that the gift be given to the Bar Mitzvah boy through a third party, which the third party will pick up as a Kinyan on behalf of the Bar Mitzvah boy before Shabbos, and once it legally belongs to the Bar Mitzvah boy, the gift can later be handed to him on Shabbos.
https://asktherav.com/28989-can-i-gift-my-wife-jewelry-before-i-accepted-shabbos/