A motion supporting the name change was passed at a meeting of Derry City and Strabane District Council on Thursday.
The council will now write to the environment minister to seek clarification on how to go about the change.
All previous attempts to change the name have failed.
The London prefix was added to Derry when the city was granted a Royal Charter by King James I in 1613.
In 1984, the name of the nationalist-controlled council was changed from Londonderry to Derry City Council, but the city itself continues to be officially known as Londonderry.
The issue was addressed in the High Court in 2007 when the judge ruled that only legislation or Royal prerogative could change the city's name.
On Thursday, Sinn Féin councillor Eric McGinley brought the motion to the council.
"In the previous Derry City Council there was a clear policy to change the official name of the city back to Derry.
"Unfortunately that proposal was defeated by the DUP and SDLP so we're simply revisiting the issue and yesterday's decision now seeks again to change the official name."
Mr McGinley added that the proposal was not about airbrushing London from the history of the city.
"We have a clear view that the city needs a clear brand, one single name, one single identity would help promote the city around the world."
DUP councillor David Ramsey said the motion was simply another attempt to stir up tensions.
"If republican and nationalists politicians in the city are serious about equality and a shared future we should be celebrating our connection with London.
"We should also be celebrating our diversity of our British and Irish cultures and history which includes the historical name Londonderry after the stonemasons who built the city.
"It creates sectarian tension and how does this reflect upon the nationalist republican goal to achieve a shared future?"
DUP Foyle MLA Gary Middleton condemned the proposal and claimed Sinn Féin had introduced it to distract from their "illogical position on welfare which is taking £2m per week away from frontline services".
He said the matter had already been ruled upon by the courts.
"In 2007, Mr Justice Weatherup ruled that the city charter could only be changed by prerogative or legislation," he added. "The council is irrelevant to the name of the city.
"Therefore no matter how much Sinn Féin want to change the name of the city, they know that they cannot."
Ulster Unionist councillor William McCandless said the "official name of the city is Londonderry".
He said it was a name that "unites the two communities -  London for the British tradition and Derry for the Irish tradition".
"Indeed many unionists are quite prepared to use 'Derry' as a shorthand term in everyday speech, but they are in no doubt that for official purposes the full name of the city is Londonderry," he added.
A proposal by Sinn Féin to change the official name of Londonderry to Derry has been described as "sectarian" by unionists.