so letss consider first example
Jazz pianist and composer Thelonious Monk ... --> correct
In above example composer is the noun which prefaces the noun Monk.
Then what is Jazz pianist referring to.
if there's an article, you DO use a comma.
if it's an adjective, you DO use a comma.
example:
Jazz pianist and composer Thelonious Monk ... --> correct
A jazz pianist and composer, Thelonious Monk ... --> correct
Creative and original, Thelonious Monk ... --> correct