Echeveria 'Perle von Nurnberg'

Melissa, It appears to be a Graptopetalum paraguayense, or has some in it (there are lots of hybrids). There's a lot of information here already written on rooting cuttings (use the search box at the top of the main Cactus and Succulent Forum page), but basically, no water except for misting the cutting, the cut end slightly inserted in the soil, lots of light (eventually full sun, but not yet), warmth, air movement and it should be growing in a month or so.

Double post- HERE - Melissa That plant looks quite etiolated - it isn't receiving enough light. You can pot up pruned off piece and it will grow roots. It is also etiolated, so I would take few leaves off and shorten the stem little. Let callus for a hour or so, and insert into dry mix. Do not water for a while, roots will start growing quite fast. Once there are roots, plant should be watered regularly - when mix is almost completely dry throughout. You can tell by (usually) new growth, or plant being quite firmly in the mix when gently tugged on - best is not to disturb plants new roots by pulling it out :) Leaves will most likely grow into new plants - just put them on top of mix. They could be just resting on it, with end that leaf was attached to the stem touching surface of mix. Some ppl push them into mix just a bit.. Do not water for at least a week or two. Sometimes roots will grow all over the place, sometimes right into mix. Keep both (cutting and the leaves) in bright spot but not direct sun for a while. After about 10 days or so, put them into bit more sunlight, and increase amount every coupe of days. Succulents need lots of excellent light, otherwise they will grow skinny, lanky, with leaves spaced far apart and pale in color. I am not quite sure what is your plants name, since I think it is growing in low light and not true to what it should be. Generally, most succulents need lots of light, all need good drainage.

Left plant could be Echeveria shaviana or another frilly type (Neon breakers is another I can think of right now). They supposedly get more frilly in great light. IIRC, Neon breakers could get more colorful, with pinkish-reddish margins. The middle plant could be E. gibbiflora metallica, or PvN as you suggested - they could look very similar. I am not sure about plant on right. I see plastic liner - make sure there are drainage holes in it. Give plans great drainage, good sunlight and hopefully they grow to be easier to ID.