From ragaTheDude.
First there are 2 very different applications of gotra system. Laukika and vaidika. Lot of questions will automatically be answered if you are aware of the differences and know the context. A gotra can be defined as an exogamous unit of an endogamous tribe. A clan or family.
Laukika application
- Marriage rules - a Male and female of same gotra cannot marry as they are considered siblings.
- Adoption rules: childless couples should really adopt someone from same gotra (shortcuts you see in modern days to violate rule #1 are wrong). +++(However: Vitatha Bārhaspatya (Bharadvāja) was adopted by Bharata Dauhṣanti upon destruction of his properly Kṣatra progeny (thus B -> an unstable B/K).)+++
- Levitation+++(←नियोगः?)+++- kalivarjya, so no need to go there.
Note that there’s no Rishis involved here. This kind of tribe endogamy with clan exogamy was seen throughout the world.
Vaidika application
Vaidika application is only in ritual context:
- How many cuts to your havis - rules vary between bhargava gotra and others
- Apri sukta and pravara recitation
- Should the oldest Rishi of the pravara mentioned first or the recent one - differences based on hota or adhvaryu
- Atreya should be brahma (not uniformly accepted).
- Certain mantras by vishvamitra avoided by folks of vasishtha gotra.
The pravara rishis have to be mantra composers. So kshatriyas and vaishyas long back if they had mantra composers will have Rishi gotra and can use it in vedic rituals - Based on pururavas aila for kshatriyas and vAtsapri bhAlandana for vaishyas. In practice for using gotra of purohita’s gotra is allowed for vaidika purpose. For marriage and other matters you use the laukika gotra.+++(5)+++
Gotra names even for brahmins need not be a Rishi - just an illustrious member. For e.g there are while group of yAska gotra ganas after the nirukta author. However he’s not a Rishi. The pravara list has bhrigu, vaitahavya and sAvetasa the actual mantra composers. The pravara list has bhrigu who’s not even biologically related rather than yAska a famous personality in his own right. (Vaitahavyas were kshatriyas- adoption of kshatriya lines into kevala bhargavas/angirasas is a separate topic.)