Nomenclature
The naming of astronomical bodies is controlled by the International Astronomical Union (IAU), which normally names features on planetary surfaces after people, and then lays down strict standards for this naming – craters on Mercury, for example, are named after "famous deceased artists, musicians, painters and authors". However, the right of choosing names for asteroids is given to the discoverer, pending IAU approval. This tends to produce an idiosyncratic collection of names – whilst many are named after mythological figures, or prominent astronomers, many more are named after popular musicians, obscure historical figures, or personal friends of the discoverer.
The IAU does not name stars, and has no intention of doing so; proper names are rarely if ever used by professional astronomers, and so there is no need for them to. Whilst many private companies will offer the "right" to name a star, for a fee, they have no legal standing to assign any star a name, and can offer no guarantee of the name being noted.
Leaving aside these attempts, the stars named after individuals fall broadly into two groups. The first group, mostly older stars, are those named openly for an individual connected with them in some way. The second, somewhat more obscurely, are those named after an individual but without explicitly making this clear.
Read more about this topic: Stars Named After People