It's probably a bit different from what you meant, but I'm pretty sure Halti, Haglöfs and Fjäll Räven have to be up there as most popular. It seems that every Finn, who does any outdoor activities / sports (and that's a lot) wears something from these brands. Also Fjäll Räven seems to be also worn as a fashion statement by the younger hippie crowd.
Other than those more visible outdoor brands, I don't really even know the brands of my own clothing, let alone other people's. :)
I'm not sure if any single brand is more successful than another, I feel that the shops you get the clothes from (f.ex. H&M, Vila, Lindex, Vero Moda) mean more to the average shopper... When talking about finnish clothing, I have to mention Marimekko, but I feel the prices are too high for it to really be a major, popular brand that most would own?
I found this list "Tommy Hilfiger, Michael Kors, Hollister, SuperDry, Abercrombie & Fitch, Brandy Melville, Benefit, Victoria's Secret, Gant" from a forum thread a few years ago discussing popular clothing brands for teens. I haven't even heard of half of these (and honestly was kind of surprised to see Victoria's secret there, I always had the image of that as a brand for thirty-somethings but I guess that just shows how out of touch I am 😂), so I don't know how legit these are. I do think Abercrombie & Fitch and Hollister are still quite popular. I think the younger people here are more intested in brands thanks to fashion vloggers etc than people my age, but it probably depends a lot on the person. Out of the people around my age group (30+) in my circle of friends the only ones who are interested in clothing brands tend to like Japanese brands like Liz Lisa - but I feel this is something particular to my circles 😅 Out of older people, those who have money probably go for brands that are internationally famous, or buy Marimekko.