I'm in 1436 and I started in 1399, recently I noticed that I got a new king and he's apparently under the same dynasty as the Muscowy king? What is going on? Is this bad?
No, it's just that your king is in the same family as the one in muscowy. It give +3 relations to Muscowy every yearThe two countries are in the same dynasty
If you have no heir and lower prestige than Muscovy AND a royal marriage with them then it will increase the likelyhood of them leading a personal union with you on your monarch's death.
But if you get an heir you will carry on the Muscovite name with no ill effects. If having a non-Swede on your throne irks you, allow some pretenders to break your country. Then you'll get a new Swedish royal family.