Sarkozy's party currently bears the title Union pour un Mouvement Populaire (UMP), which translates as the less-than-catchy Union for a Popular Movement.
When he was campaigning to be elected party leader in 2014, the former president declared his intention to give the party a complete makeover.
That included scrapping the name it adopted in 2002 ahead of Jacques Chirac's successful campaign to be reelected president.
Sarkozy himself stood under the UMP banner in 2007, when he won, and in 2012, when he lost.
Since that painful defeat, the party has been going through some rough times, with a damaging row over its first leadership election, several of its leaders, including Sarkozy himself, facing legal investigations and stiff competition on the right from Marine Le Pen's Front National.
So, time to put all that behind them with a change of brand.
With its reference to the "republican values" French politicians love to invoke - although not always define - Les Républicains seemed to be just the ticket.
But left-wing politicians and lawyers don't see it that way.
They think the right-wingers are effectively declaring themselves the only republicans in town and have gone to court to try to prevent that happening.
Sarkozy and friends want to "privatise the republican ideal", they argue, and that amounts to stirring up "major civil, social and political trouble".
"No part of the French people can claim the exclusive use" of the term, they say.
The case is to be fast-tracked and go to court on 22 May ahead of an internet vote of UMP members due to take place on 28-29 May.
At first UMP supporters didn't seem convinced, either.
An opinion poll last month found more than half of them judged the name "too American", although a new one this week seemed to show they had changed their minds, with 61 per cent backing it.
The same poll found that 61 per cent of all those asked didn't find the choice of name shocking, although Socialist and hard-left voters most definitely did.