Marine Le Pen declared the result of a questionnaire sent to the 51,000 members the party claims "reassuring", particularly since they were commenting on the principle of a name change without knowing what the new one might be.
A "small majority" of those who replied - 27,000 according to Le Monde newspaper - who replied supported the idea, she said.
But her father, former party leader Jean-Marie Le Pen, on Friday accused her of lying about the result.
"Internal sources" contradicted the claim, he said, adding that the count had taken place behind closed doors.
"In these conditions, favourable to the most diverse manipulation, it's impossible to give any credit whatever to Marine Le Pen's statements," he said.
Other anonymous party members also cast doubt on the result, the AFP news agency said.
Undeterred, the current party leader and former presidential candidate is to propose a new name in her closing remarks to this weekend's party congress and her proposal will be put to a postal ballot of the membership.
Not The Nationals
Marine Le Pen refused to tell reporters what she was going to propose but did rule out certain words - "front", because it sounds too "military", and "The Nationals", which has been suggested by far-right MP Gilbert Collard, because she is not thinking of anything in the plural, bucking the current trend on the French right.
She will also not be picking "The Patriots" , which, apart from being in the plural, sounds "old-fashioned" to her.
Its main disadvantage, however, is that it is already taken by the new party of Florian Philippot, the former right-hand man to Marine Le Pen who split from the FN in the aftermath of last year's disappointing election results.
Rebrand but no policy change
Launching the name-change process and reelecting Le Pen as leader unopposed will be the main tasks of the Lille congress, along with amending the party constitution.
Although the party leadership is presenting the conference as an "overhaul", major policy changes are more or less ruled out and the change of line on leaving the euro - one factor in Philippot's departure - is not set to be reversed, although not all party members seem to be happy with it.
Rebranding is a continuation of Le Pen's efforts to clean up the party's image, launched when she took over from her father in 2011.
It is her main weapon in her strategy of winning over right-wing voters who may agree with the party's ideas but be put off by Jean-Marie Le Pen's legacy.
Setbacks since presidential election
That plan has taken a beating since her peformance in the presidential election debate with Emmanuel Macron, which was generally judged to be disastrous.
A recent opinion poll, published by Le Monde, showed a decline in Marine Le Pen's popularity over the last year, with the number of people believing she would be a good president falling from 24 to 16 percent and the number who believe she understands their problems falling nine points to 40 percent.
Since the elections Philippot has split amid mutual recriminations and Marine's niece, Marion Maréchal Le Pen, who was one of two far-right MPs in the last parliament, has announced her retirement from politics.
That would not necessarily be bad news for her aunt, since Maréchal Le Pen is the darling of the Front's Catholic, traditionalist wing, but it did not prevent her addressing a conference of US right-wingers last month so may well be just a temporary state of affairs.
The spectre of Jean-Marie
Meanwhile, Jean-Marie Le Pen refuses to kindly leave the political stage.
He has described the name change proposal as "suicidal", just one of many slights on his daughter's running of the party.
The 89-year-old political scrapper, who was expelled from the party in 2015 but by court order remains its honorary vice-president, has just published the first volume of his memoirs, with an exceptional 100,000 print run.
He can now boast that his book has sold more copies than volume four of Elena Ferrante's wildly popular Naples novels, which has also just been published in France.
But at least he has dropped his threat to turn up at the congress, although his political ghost will no doubt haunt the meeting hall this weekend.