The DUP says it will support the use of the Irish name of Derry on all official personal documentation providing that the official name of the city remains Londonderry.
Assembly member Willie Hay said the DUP found it "perfectly acceptable" for residents of the city to have it called Derry or Doire on documentation providing that no move was made to change the official name of the city.
His comments came ahead of likely agreement between Sinn Féin and the SDLP on name change proposals to be put before tonight's meeting of Derry City Council.
While both nationalist parties want the official name of the city to be changed from Londonderry to Derry, they differ on a timeframe and methodology.
Sinn Féin wants a commitment to change with a plebiscite if necessary, to be adopted tonight, while the SDLP says the name change should only come about after equality, community relations provisions and legal implications have been considered.
Both existing motions endorse the principle of residents to refer to the city according to their own wishes, including on official documentation.
But with senior SDLP and Sinn Féin councillors due to meet again today, there were hints last night that a common position and composite motion would be agreed between the parties before tonight's meeting.
The SDLP was also due to meet unionist councillors last night in an effort to explain and attempt to gain support for its motion. SDLP council group leader Pat Ramsey there was "very little water" between his party and Sinn Féin on the issue but unionists should not feel excluded because of any name change.
"It's fair to say that there seems to be a coming together (with Sinn Féin) which may result in a motion which all parties can support," he said.
Sinn Féin's Barney O'Hagan said: "I am confident that at the meeting the
first steps will be taken that will resolve the issue."
Mr Hay said: "The name Londonderry is historic for unionists in the city
who believe it already reflects the Irish identity.
"We believe it is perfectly acceptable for all names of the city to be recognised on official documents, including the Irish name, as long as the official name of the city remains as Londonderry."