Famous dog originally dwelling around part of Switzerland? (2,7)

I haven't cracked this one yet — but the brilliant team at Times for the Times have:

BERN (part of Switzerland) in STAR (famous) D[welling]; a nice all-in-one, even if one usually dwells in a place, not around it. Thanks to Zylanthic and Keriothe for the alternative (correct) parsing which makes my comments redundant: BERN (part of Switzerland) dwelling in STAR (famous) D[og];