Flower is cut: name? (6)
I believe the answer is:
severn
'flower' is the definition.
(River Severn)
'cut name?' is the wordplay.
'cut' becomes 'sever' (to sever is to cut or split).
'name?' becomes 'n' (common abbreviation e.g. on forms).
'sever'+'n'='SEVERN'
'is' is the link.
(Other definitions for severn that I've seen before include "River rising in Wales" , "GB's longest river" , "River with famous bore" , "Welsh and English river" , "Major UK river" .)