They have the 1430 in their logo so I would guess they could be the original mint, most likely changed places multiple times in the last centuries. But I don't find anything concrete on their quite sparse webpage.
‘Bratislava / Preßburg / Pozsony, Slovakia’ is a location not a name so yes if they are in fact an iteration of the original mint, adding the most recent name might be a good idea even if it would be anachronistic in the context of medieval times. Maybe there is something written in the guidelines?
For your information ß = ss.