New name used by oil supplier to show good intentions (4,4)
I believe the answer is:
mean well
'show good intentions' is the definition.
'new name used by oil supplier' is the wordplay.
'new' is an anagram indicator.
'used by' is a charade indicator (letters next to each other).
'oil supplier' becomes 'well' (oil well).
'name' is an anagram of 'mean'.
'mean'+'well'='MEAN WELL'
'to' acts as a link.
(Other definitions for mean well that I've seen before include "Want to he helpful" , "with good intention" , "Having intention to act properly" , "aim to please" , "Have good intentions but poor performance" .)