Local MP Ian Lucas said people were concerned about the impact it could have if the prison on Wrexham Industrial Estate assumes a local name.
In a letter, prisons minister Jeremy Wright says local names are "generally avoided as most local people object".
He said it was likely people would be invited to propose names for the Â£212m prison which is due to open in 2017.
Work is expected to start in August, creating up to 1,000 jobs, to build the prison which will house 2,100 inmates, making it the largest prison in the UK.
The overall project spend is lower than the original Â£250m estimate and the construction will involve local business and enterprises, with 100 apprenticeships created.
Wrexham's new super-prison is unlikely to be named after the county borough, says the prison minister.