HUMZA Yousaf has admitted he struggles with the name of the SNP and its associations "because of the connotations of nationalism".
The Justice Secretary said he would have chosen a different name when the party was formed.
His comments echo those made by First Minister Nicola Sturgeon in 2017, who said she would change the name if she could turn back the clocks.
Yousaf was taking part in an on-stage interview during the Edinburgh Festival Fringe.
Asked by an audience member if it is time to drop the "national" part of the SNP, he said: "I do struggle with it, because people do associate it with all the various elements of nationalism that exist.
"But the SNP, when the name came into being it was meant to be the national party of Scotland – not just for one particular part of Scotland, but it would cover everything.
"I think the brand is so strongly associated that a name change would be difficult and challenging.
"But I think if I was in those discussions when the SNP was made, I would have thought of perhaps looking at a different name because of the connotations of nationalism."
He added: "Now, for me, I don't think anybody that really knows the SNP, knows the people involved in the SNP, knows the core of the SNP, thinks that we are associated at all with that nasty, right-wing nationalism, at all.
"Not to say that there aren't bad apples who support us and whatever else, and we must weed them out, root them out.
"But the core of where we are is nothing to do with those nefarious elements of nationalism.
"I think people understand that we are an open and inclusive party.
"But do I think that the name can present us with some challenges? For sure."
Sturgeon previously said the word "national" can be "hugely problematic".
Speaking at the Edinburgh International Book Festival in 2017, she said: "If I could turn the clock back, what 90 years, to the establishment of my party, and choose its name all over again, I wouldn't choose the name it has got just now, I would call it something other than the Scottish National Party."
Elsewhere, Yousaf insisted it would be "utterly foolish if not downright stupid" if the independence movement did not learn lessons from the disastrous Brexit process.
He said: "We have to learn that and understand that when it comes to Scotland becoming independent and when we do become independent – we will become independent, there's no doubt in my mind in the slightest about that – that when we do, that we must understand there's a range of opinions out there, there will have been people that will have voted no, and take them with us.
"So not going to extremes, which is what Theresa May did to try to appeal to the hard Brexiteers, not going to the fringes.
"Not going to extremes but taking people with us, is going to be a hugely important part of that process."
He said the Yes movement "has to look at the arguments and where we lost the arguments".
He added: "Person after person said to me that the economic case was just not strong enough."
However, Yousaf insisted the Growth Commission – the SNP's controversial blueprint for independence – paints a "realistic picture".
He said: "It doesn't tell you that independence is going to be a land of milk and honey, because it ain't.
"We are going to have challenges, like any other country has."
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