Booze 4 U in Stretton, near Burton, had already been told that its garish sign – which prominently features the word “discount” – would have to be changed because it fell foul of planning regulations.
Now Dippa Dehal, 35, and his cousin, Jack Somal, 32, are asking customers to come up with a more suitable name for the shop, which previously traded as Main News.
Customers will have until July 1 to choose between for Stretton Village Stores, Spend 'N' Save, Stop 'N' Shop, Select 'N' Save or One Stop Village Stores.
The businessmen admitted they underestimated the reaction their original name would generate in an area already plagued by youth drinking and antisocial behaviour.
Recent months have seen several cases of local residents objecting to licences for new off-licences with names they considered downmarket or which seemed to emphasise cheap alcohol. Bargain Booze has faced a number of such challenges but has pointed to its strong track record in combating under-age sales.