Hi,

Yes, I've visited the stadium several times and you're right about the signs. The stadium is indeed often called BORUSSIA-PARK. But technically, the football fields located next to the stadium and the biergarten also belong to BORUSSIA-PARK. You can contact the official club page for confirmation. The stadium itself, which is part of BORUSSIA-PARK, is officially named "Stadion im BORUSSIA-PARK". The stadium tag only includes the stadium area, not the entire BORUSSIA-PARK area. I've made a tag which includes the BORUSSIA-PARK, which is technically a sports complex.

Here you can find some reliable sources:

http://stadiumdb.com/stadiums/ger/borussia_park
https://www.transfermarkt.de/borussia-monchengladbach/stadion/verein/18
https://footballtripper.com/germany/borussia-monchengladbach/
https://germanfootballgrounds.com/clubs/gladbach/

I hope this will clear things up.

Have a nice day!