Answer

Yes — “Jakh” is used as a Jain gotra name in some regional Jain communities, especially among Punjabi Jains. Jain gotra usage is not uniform across all Jain groups, so it may be recognized in some lineages and not in others. ( en.wikipedia.org)

Explanation

Jain gotra lists vary by community and region. The sources I checked show Jakh in a Punjabi Jain context, while other Jain gotra lists are broader and not exhaustive, which means a gotra can be local or lineage-specific rather than universal. ( en.wikipedia.org)

Takeaway

So, if your family uses Jakh as its gotra, that can be a genuine Jain family gotra tradition. ( en.wikipedia.org)