Stellar designation takes a number of forms, often developed through history as more stars came to be observed and systems of designation that reasonably deal with the larger number came to be needed. Stars brighter in the sky and known for a long time often are known by older designations, and dimmer, more recently discovered stars, by some newer system.
A few stars have traditional names. Bayer designation and Flamsteed designation were two methodical approaches introduced after telescopes came into use. Designators have come to be used for recent discoveries by large surveys using modern research telescopes. For a few examples including both bright stars and more recently-discovered dim stars (nearby red dwarves and brown dwarfs), see list of nearby stars.
Variable stars have their own variable star designation.