noun
accredited master; licensed performer
Specifically refers to someone who has been granted a professional stage name in traditional Japanese performing arts like Noh, Kabuki, or Japanese dance, signifying a recognized level of mastery.
彼は去年、名取になって、自分の名前で舞台に立つようになった。
He became an accredited master last year and now performs under his own stage name.
noun
fame; popularity; famous person
A less common, somewhat literary usage referring to the state of being famous or a famous person. In modern Japanese, 有名 (ゆうめい) or 有名人 (ゆうめいじん) are far more common.
その作家は若くして名取を得たが、その後作品を発表しなくなった。
The writer gained fame at a young age, but stopped publishing works afterwards.
Compound of 名 (な, 'name') and 取る (とる, 'to take'), literally 'name-taking'. The accredited master sense comes from the tradition of granting a professional name to a student who has reached a certain level.