Humza Yousaf has claimed he is not "comfortable" with the name of his own party.
The Scottish National Party's leader said the word "national" could be "misinterpreted".
He said: "I've never really been comfortable with the fact that we have national in our party's name."
Yousaf said he doesn't believe any founding members of the party had any "far right nationalist inclination", telling the BBC his party had developed a "very strong brand" based on "civic" nationalism".
Humza Yousaf has claimed he is not "comfortable" with the name of his own party
PA
The First Minister explained: "We're a party that believes it doesn't matter really where you come from - what's important is where are we going together.
"And there's no doubt about our politics being very routed in the left and the centre-left of political discourse."
In 2017, Yousaf's predecessor Nicola Sturgeon said she would have changed the name of the party is she could "turn the clock back", saying that the word "national" can be "hugely problematic".
Yousaf also said that the police investigation into the SNP has impacted the party's reputation.
He said: "The police investigation has been one of the most difficult times for the party.
"There's no ifs or buts or maybes about it.
"There has clearly been an impact in terms of how we were perceived by the public and issues of trust and I've got to work hard, as I hope I have been doing over the last ten months.
"I've got to work hard to make sure that people know, whatever the outcome of that police investigation is, that the SNP is a party that they can trust."
He added: "It's been difficult, no doubt, for those involved.
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"But difficult for us as a party and it's certainly been a challenge for me in my first ten months."
Sturgeon, along with her husband Peter Murrell and party treasurer Colin Beattie were all arrested and released without charge as part of a police investigation into SNP finances.
Operation Branchform is investigating £600,000 raised by the party for independence campaigning.