In which major league do the Rajshahi Warriors compete?

They participate in the Bangladesh Premier League (BPL), one of the top professional Twenty20 cricket leagues globally, though sometimes under different franchise names.

Have the Rajshahi Warriors (or their previous iterations) won any BPL titles?

Yes, as Rajshahi Royals, the franchise won the Bangladesh Premier League title in the 2019-20 season.

What other names has the Rajshahi franchise used in the BPL?

The franchise has previously competed as Rajshahi Kings, Rajshahi Royals, and Duronto Rajshahi in various Bangladesh Premier League seasons.