Finnish names are cool, full stop. People who can't appreciate them are just missing out on that coolness. Glad to hear you are not giving in to the doubters!
What's more trouble do you think Anniina, the double letters, or the umlauts and rings? Some ä or ö or å anyone? Those aren't even on keyboards, except in the relevant countries. And I wonder if they were even part of Finnish, before the Swedish occupation?
My maternal grandfather was a Swedish-Finn immigrant to the USA in the early part of the 20th century. His last name had both ä and ö - Söderäng ('south meadow'). He got some advice from more experienced immigrants - "they'll make hash of that at Ellis Island! Have a plan to avoid that." He chose to use the last name from another branch of his family, 'Vest', which means 'west', and not surprisingly got spelled with a 'W' when he was processed into the USA. So his family all had West for their last name. But at least he (and they, including my mom) didn't end up with some awful mangling like "Suddering" or "Soldering" or "Sowdarung" and so on...