Could anyone tell me the name of this plant?
This is not a flower, it's a plant. I think it's an Echeveria of some description, either that or one of the Aeoniums - it's hard to be sure what it is because it's in such poor condition.
Whichever one it is, the care regime is the same; these are succulent plants, and are best kept on a windowsill which receives some sun indoors, although they can go outside during the summer months in colder countries, and may grow outside year round in warm countries. They like average warmth, but need cooler temperatures (50-55 deg F) in winter, and prefer a marked difference between day and night temperatures. They should be watered when the surface of the potting soil feels dry to the touch and watered well from spring through to fall, but watered very sparingly in winter, maybe once every 1 or 2 months. Good drainage is essential, and the plant should not be left in any outer tray or pot with water in it, so empty that out 30 minutes after watering. If the plant is indoors, it will like some fresh air, so an open window nearby is helpful.