Uncommercial name for mostly tinpot organisation (3-6)
I believe the answer is:
non-profit
'uncommercial' is the definition.
(I've seen this before)
'name for mostly tinpot organisation' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'mostly' means to remove the last letter.
'organisation' indicates anagramming the letters.
'tinpot' with its final letter taken off is 'tinpo'.
'for'+'tinpo'='fortinpo'
'fortinpo' anagrammed gives 'onprofit'.
'n'+'onprofit'='NON-PROFIT'
(Other definitions for non-profit that I've seen before include "characterising a charity?" , "Uncommercial" .)