I'm in Finland and we actually have a police officer
who's gotten pretty famous. He's a pioneer of online police work (like having a presence on social media and making it easier for teenagers for example to report things like sexual harassment online) and so he's the expert (it seems that in a small country there's room for only one expert in a given field) for all sorts of information about children's internet use and things like that.
I assume that in some ways fame here is similar to larger countries, it's just probably easier to become a national celebrity (much of our media is national). There's fleeting celebrity often created by tabloids, people who predict the weather based on behavior of frogs (the Toad Professor), people who try to break records drinking soda on tv (Kola-Olli) and people who will drive across the country on a mini-tractor, if enough people like their Facebook page. People may remember their tabloid nicknames years later but the actual fame fades pretty quickly.
Then there are people who seem to be famous for strange reasons. There's for example a woman
whose affair with a minister caused his resignation, five years later she's still famous for mostly behaving badly in public. Another example is an Estonian woman who married a Finnish designer and whose main job is to tell Finnish women how ugly and fat and unstylish they are (and how much better Estonian women are in every way, they even gain weight better). She sells a lot of magazines. Finns seem to like tragic stories, especially when it involves alcohol. Possibly the most famous of the tabloid celebrities is Matti Nykänen
, once one of the most successful ski jumpers in the world, these days an alcoholic who seems to make his living by being in tabloids with his dysfunctional relationships
, jail time (for assaulting his wife, among other things) and other screw-ups.
For lasting fame you probably have to achieve something. There are the politicians, actors, writers (like Sofi Oksanen
who's a good celebrity on top of being a good writer, not really for the tabloids but she's recognizable and opinionated), musicians and so on. We possibly have more celebrities as politicians as some other countries, famous people will often get asked to be candidates by different parties as it's assumed that they will get votes just because they're well-known and because of the voting system they will benefit other candidates too and so we have had members of parliament who used to be athletes or models or actors or singers and one MTV Europe VJ.