Every puja begins with a sankalp: a short statement of intent spoken by the priest, or by you, before the ritual starts. It says who the puja is for, where and when it is being performed, and the purpose it is offered with.
Traditionally the sankalp names the person or family, their gotra, the place and the date according to the Hindu calendar. Saying it aloud connects the ritual to the people it is meant for. That is why a priest will ask for your full name and gotra before he begins.
Your gotra is your family lineage, traced through the paternal line to a rishi. Many families know theirs from elders or from family records. If you do not know your gotra, it is common practice to use Kashyap gotra, and priests will guide you on what is customary in your tradition.
On Aaradhya, your sankalp details are confirmed back to you before the puja, and the proof pack includes the sankalp read aloud with your family's names and gotra, so you can hear for yourself that the puja was performed for you.