I agree with Haworthia, possibly H. attenuata. I can't tell what the flowers look like. This is the flower from my plant.

The one on the left appears to be a Mammillaria, but not prolifera. Maybe M. rhodantha pringlei? The one on the right might be a Pilosocereus, but it is hard to say what kind until it is larger. P. baumii is not a recognized name, although Altman Growers sells plants under that name which end up in most of the big-box nurseries. On this Cacti Guide thread the consensus was that it might be P. gounellei.

Could you post over on the Cactus and Succulent forum? You'll get a reply there. I'm guessing mammalaria something, but others know much more than I do. You didn't ask, but I'll take the liberty of saying it needs to be repotted higher in the pot so it can get more light. Pot size is probably ok. The experts on the cactus & succulent forum will recommend commercial cactus/succulent soil mixed 50/50 with perlite.

Left-Hard to tell, but looks like a Mammillaria. What species not sure:). Middle- Echinocactus grusonii aka Golden Barrel Right- Stetsonia coryne aka Toothpick Cactus All of these guys need a fast draining mix. Most store bought cactus mixes need to be amended with perlite and or pumice. Since they are small and you only have three perlite and cactus mix will be fine. Pumice can be hard to find in stores if you don't live in California. I have no idea why;). A mix of 60% perlite and 40% cactus mix will do. The containers they are in now look like the right size. Make sure they have drainage holes. When repotting get all the old soil off roots. Rinse the perlite off because it can be dusty. You can use an old kitchen strainer. Then just pot up like any other plant;). Don't water for a week after repotting. Since winter is near it's time to put these guys to "sleep". So I would give them that one drink and then keep dry till spring. They will be fine:). Most cactus go dormant during the winter and so it's important to keep dry. When spring comes around you can begin to water once a week or every ten days. Just make sure the mix is thoroughly dry before giving another drink. When it comes to light in the winter just keep near a bright window. As long as you keep dry you shouldn't get much if any growth. When March comes start acclimating to more light slowly. Eventually they should be in full sun during the warmer months. Goodluck:).