The petition calls for a temporary landmark to commemorate new film, "Ali G: Who Iz I?".
Spelthorne Borough Council has a vision for how Staines will change and grow over the next 15 years.
Councillors vote to seek a new name reflecting Spelthorne's Middlesex heritage.
Councillors propose re-naming the new authority West Surrey and South Middlesex.
Woking and Spelthorne are facing financial difficulties, including large debts.
Spelthorne Borough Council says the new area in Staines Park will open on 21 July.
Concerns over development at Kempton Park fuel debate about housing spreading into the countryside.
Spelthorne Borough Council, which owns the Sunbury site, says the firm will be "sadly missed".
Councillors had argued that Middlesex predates the Domesday Book and should not be erased.
