The genus Sempervivum was named and described as such by Carl von Linnaeus in the first volume of the first edition of Species Plantarum in 1753. He wasn’t the first to name the genus as they had been known long before.
Plants of the World Online by Kew lists 51 species in the Sempervivum genus (as of 2-22-21 when I last updated this page). it is a member of the plant family Crassulaceae with 26 genera. Those numbers could change as updates are made (and likely will).
There are several great websites online about Sempervivum, I will just add a few of their links instead of doing a big write-up. I am not an expert, by far. I just like growing plants, taking a lot of photos, and writing about them. This is a parent page for the Sempervivums I have grown.
Sempervivum are great plants once you figure out what they want. I have grown six different species and cultivars and some have been very tricky and eventually fizzled out. The only one that has remained is Sempervivum ‘Killer’ which I planted in the ground. The others I had in pots and I brought them inside for the winter. I think by far the reason most of them fizzled out was because of soil moisture. In pots, they were in a mixture of Miracle Grow Potting Soil amended with additional perlite and chicken grit (2-1-1). Peat stays damp for a while once it is soaked and the soil was usually too damp when I brought the pots inside and put them in the basement over the winter. The Sempervivum in the ground is in a planter that drains well in ordinary topsoil. The secret to growing Semps is for them to be in well-draining soil. They like ample moisture during the summer as it rains, and maybe a little supplemental water when it is hot and dry. Even though we do get plenty of moisture during the fall and winter, it still survives and returns the next spring. I will keep trying to grow more because they are great plants. I just have to figure out how to get those that are not reliably winter hardy here in west-central Missouri (USDA Zone 6) to overwinter inside.
There are HUNDREDS, one website says over 4,000, named cultivars of Sempervivum. Many cultivars look so much alike, so if you bring home unnamed plants trying to figure out the name is nearly impossible. Most of what you will find are cultivars of Sempervivum tectorum.