When a person attends a puja or yagya there is a point at which the sponsors of the event are recognized and their names are read. This is called sankalpam, or the statement of purpose. In this, a person is known by their name, their gotra, and their nakshatra (vedic constellation).
For westerners we can state our name and nakshatra but knowing what to say for the gotra has always been a problem. Traditionally every family traces their lineage back to one of the original rishis of the Vedas. But westerners obviously can not do this.
I recently met a North Indian priest and when he ask me my gotra, I I just shrugged and he said that a westerner should always use “Kashyapa” as a gotra. From the perspective of the vedic tradition, Kashyapa was the father of the devas and asuras and and all of humanity. He is married to Aditi with whom he is the father of Agni. He is also the father of Surya, the sun.
So from that perspective, we are all descendants of Kashyapa rishi.