Record company name left with guy in Genesis (5)
I believe the answer is:
label
'record company name' is the definition.
'left with guy in genesis' is the wordplay.
'left' becomes 'l' (common abbreviation).
'with' says to put letters next to each other.
'guy in genesis' becomes 'abel' (biblical character).
'l'+'abel'='LABEL'
(Other definitions for label that I've seen before include "Identification tag" , "Identify" , "Classifying name" , "Tag or trade name" , "Name-tag" .)