At a meeting of the city council on Tuesday night, the Sinn Fein motion was dropped in favour of an SDLP amendment giving equal status to both names.
The Ulster Unionist Party had urged Sinn Fein to reconsider its proposal to "remove the London from Londonderry".
Sinn Fein brought a motion before the nationalist dominated Derry City Council on Tuesday night calling for the city's official name to be established as Derry.
The dispute over the naming of the city has been running for decades, with nationalists and republicans using the name Derry, while unionists and loyalists use the name Londonderry.
Before Tuesday's meeting, South Down Ulster Unionist assembly member Dermot Nesbitt appealed to Sinn Fein to give up their "divisive" plan.
Mr Nesbitt, the former environment minister in the now suspended Northern Ireland Executive, said he believed the move by Sinn Fein was illegal.
"Article 75 of the Northern Ireland Act imposes a duty on councils to promote good relations, and clearly this Sinn Fein motion is contrary to the law, and they know that in any event only parliament can change the name of the city," Mr Nesbitt said.
"This has implications for the whole council and all the ratepayers in Londonderry.
"They would be advised not to sleepwalk into some kind of republican nightmare which will not only be contrary to the act, but be divisive and wrong."
'Marketing identity'
Sinn Fein councillor Barney O'Hagan said it had been shown by various consultants' reports that in marketing the city "there is a problem with the mixed message we are sending out over identity".
But Mr Nesbitt said: "Sinn Fein's assertion that the move is designed to establish a clear corporate civic identity is utter rubbish.
"What this is really all about is republican dominance and an unwillingness to accommodate Protestants and unionists."
The Ulster Unionist Party has just two councillors on Derry City Council, while the Democratic Unionist Party has four.
Sinn Fein has 10 seats, while the SDLP has 14.
Historic row
A previous effort by nationalists to have the city officially named Derry in the 1980s failed, but led to the council changing its name from Londonderry City Council to Derry City Council in 1984.
The council name change led to protests by unionists, many of whom still refuse to call the council by its official name.
Further confusion also comes from the fact that nationalists and unionists also variously call the city's namesake County Derry or County Londonderry.
The council itself does not have the power to change the name of the city - it is understood it can only be done by the Queen on recommendation from the government and would need an Act of Parliament.
The name Derry was derived from the Irish Doire, meaning oak grove.
Derry was formally renamed Londonderry with the granting of a new royal charter in 1613, during the British Plantation of Ulster.
During years of contention over the name, Londonderry/ Derry was named Stroke City by those who felt the row was puerile.