The tribe says the term "squaw" is racist and sexist toward Native American women.
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Tribal leaders say they have been contemplating the change for a while, and there has been discussion about switching the name to Nim Valley.
Fresno County leaders say there is still a lengthy legal process before any new name can be made official if the change is passed.
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"What I am hopeful for is I hope the ACLU really tries to reach out to the community in eastern Fresno County that they're trying to impact. Until that happens, I'm going to have to resist the efforts they are making in regards to this," said Supervisor Nathan Magsig.
"I feel that this problem with the name is only confined to the borders of S. Valley, which it's not. Names are powerful, even if unintentional, the current name is harmful," said Roman Rain Tree.
The group's next step is to finalize their petition on the name.