Hi Hugh, welcome to the forum.
You can get at least a list of species in a region of interest, if the region can be defined either as a country or a polygon of points. Start out in the occurrence search interface here: https://www.gbif.org/occurrence/
Then either choose a country, e.g. Sweden: https://www.gbif.org/occurrence/search?country=SE
Or, define a region using a polygon or geoJSON, e.g. link
Once you’ve got the area of interest narrowed down, hit download and choose species list. This’ll give you a list of all names of taxa represented by occurrences in the area.
Hope this’ll get you started!
Best regards,
Daniel