Top left may be Echeveria pulvinata and lower left possibly Pachyveria or Pachyphytum hookeri. Not positive but that should hopefully give you a start.

I would suggest that the problem is bad drainage: what is the soil like they are potted in? How about the container - is there a drainage hole (s)? How long was it raining and what part of the world are you in? (it is a good idea to indicate general location when asking for advice...best to put it next to your name so it is always there...)

Reminds me of E. nodulosa, but the growth pattern is very different. Looks like your plant has been getting a lot of sun because the rosettes are tightly closed. Once it blooms for you the flowers will give it away:).

Echeveria Pupursorum It looks like the stem is black. Is it soft/squishy/mushy? That might mean rot. So you would have to behead it. But we will get into that later, even if it is rot. If it is rot, it was caused by the soil you have it in. Also, I hope your pot has a drainage hole. It looks like what it came in.. I recommend 50/50 strained or sifted perlite and cactus and succulent soil. A drainage hole and good soil is a necessity for succulents:) Were the leaves soft before they shriveled? I had an echeveria rot, the leaves turned black and the stem was black. If it isn't taken care of soon it will rot away like mine. Trust me, it wasn't good:(