#1 is Desmodium sessilfolium (Sessile-leaved Tick Trefoil) #2 is Lespedeza cuneata (Sericea lespedeza). #3 looks like Lespedeze stuevei (Tall Bush Lespedeza) Interesting that all the plants you've posted are legumes (Fabaceae) and three of the four are Lespedezas.

Try taking samples to a local nursery. Or, maybe there is a public collection within reasonable driving distance - reasonable probably defined by how badly you want to know - that actually has the same variety, with a name.

When he pulled it out of the ground, there didn't seem to be much of a root system. I don't think it is a plumeria since it has sent up another plant next to it.

Yeah, I would tend to agree. That is something I did grow in my last garden, Solidago rugosa "fireworks" and before I posted I decided that it was developing to look very much like that was. I think that your suggestion is correct, going with my gut feeling. I was hoping for Campanula persicifolia, but didn't see that happening the past few weeks since my original post. I didn't mind my goldenrod, actually. I grew it with very tall dahlias, red ones with a gold eye, of which I don't know the name of, and they bloomed together and looked nice. I had more space then, but did bring my dahlias with me. They are sadly unplanted, but perhaps this is a push to find a place for them on the other side of the yard and I can move the suspected goldenrod out from where I don't want them and plant them all together and see what becomes of these suspects! :-) Thanks for the post, atlamol!