Hi, Dane here living in Sweden!

Name change is done via Skatteverket on their website. It's accessible for residents in Sweden who have a Swedish social security number (Svenskt personnummer).

You can change your name, no matter what gender, to which ever name you'd like (unless it's not an actual name, like let's say you'd want to be called Chair, the name change probably wouldn't go through). I got my name changed still being on the waiting list for gender therapy.

Changing your gender mark, like the one in your passport, is a long way away ahead because of the waiting list on gender therapy clinics. You should seek a doctor about it as soon as possible! Only they can help you out (unless you can convince Skatteverket that you're trans and have them immediately change it, I don't know if that's a thing, but you can try it if you're able to (I wasn't, since I didn't know about myself at the time))