Is there a word for something someone is known for?

Signature is the answer. Both as a count noun and an adjective.

[count noun] something (such as a quality or feature) that is closely associated with someone or something — usually singular

Her latest movie includes the humor and fast pace that have become her signature.

[adjective] closely associated with someone or something : making a person or thing easy to recognize

the chef's signature dish
“Respect” is her signature song/tune.
The director's new movie is a return to his signature style.

^{http://www.learnersdictionary.com/definition/signature}

Trademark: A distinctive characteristic by which a person or thing comes to be known.

E.g. (Lifted from @ermanen)...

...1-Her latest movie includes the humor and fast pace that have become her trademark.

2-The shuffle and snicker that became the comedian's trademark.

*Though "signature" would be the first thought for something that someone is particularly known for.*