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. (Albeit Caritas, probably the most famous of these, doesn't technically have it in its name.)
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.