I suggest you focus on showing that "solidarity" is a term that appears in left-wing parties names. IIRC it's traditionally associated with Catholicism, be it parties or other kinds of civic associations.
Tip: on a quick search I did find one other party that has this in its name and is left-leaning (and apparently not related to Catholicism either). And, yeah, the famous Polish labor union is perhaps interesting to mention in that regard, although they had a kind of connection with the Catholic church, even if somewhat informal. I see there's also a leftist US organization named like that (although not strictly a party), although I admit I had never heard of it before.
So, yeah, I guess you could write a fairly interesting answer on the contested/cross-sectional use of that word in party/organizations names. We did have some answers like that about other contested terms like "popular" or "people's", which were not strictly what I had asked about, but were interesting nonetheless. Albeit most answers like that were rather telegraphic.