Does the name "Magdeburger Gartenpartei" sound ambiguous to Germans, in that rather than merely referring to the name of a political party, it sounds like a party of the social kind which happens in a garden (possibly a "Gartenparty")? That is, does it have the same sort of problem the Reason Party had when it was called the Australian Sex Party?
Yes, it sounds ambiguous but for another reason than you think. There's the word
which paradoxically isn't a political party you could rent (for small money, I guess) but rather a tenant in a block of flats.
So, the first thing I thought when I heard of
was an allotment holder in a garden plot, not a political party. I think this is intended, to create that cozy feeling of having your own tiny garden.
A Fest can also be called die Party in German, never die Partei.