It could see the second division team playing as the Stirling Albion Meerkats.
The club is said to be about £1.5m in debt and has survived two winding-up orders in recent months.
The supporters trust wants to buy the club and sell its naming rights for £50,000 a year.
It says discussions with Compare the Market.com have already taken place.
However, the SFA is likely to throw out the plan.
A spokesman said: "Any proposed change of name would require to be submitted to the board for consideration and approval.
"Given that a name change for commercial purposes would have huge implications, the integrity of the game would be paramount in any decision-making process."
Source: BBC Sport
Source: BBC Sport