Gift is a short, warm word that frames bitcoin as something passed from one person to another. In German retail the English term is familiar from gift cards and gift sets, so the name reads as an invitation to give. The compound is short and easy to print on a card or a voucher, and the .de ending places the service in the German market, where vouchers are a common present for birthdays, Christmas and other occasions.
bitcoingift.de is not part of a themed set and works well as a consumer brand. Natural uses are a voucher shop selling bitcoin gift cards in retail and online, a platform for setting up savings gifts for children and grandchildren, a corporate service that rewards employees or customers in bitcoin, or a seasonal campaign by a Bitcoin app.