Adorns alternative name with odd notes (9)
I believe the answer is:
ornaments
'adorns' is the definition.
('ornament' can be a synonym of 'adorn')
'alternative name with odd notes' is the wordplay.
'alternative' becomes 'or' (**).
'with' says to put letters next to each other.
'odd' means one should take alternating letters.
The alternating letters of 'notes' are 'nts'.
'or'+'name'+'nts'='ORNAMENTS'
(Other definitions for ornaments that I've seen before include "Decorates" , "Tree embellishments" , "Tree baubles" , "Decorations, embellishments" , "Adornments, decorations" .)