Smear name around America (4)
I believe the answer is:
daub
'smear' is the definition.
(synonyms)
'name around america' is the wordplay.
'name' becomes 'dub' (as in dubbing someone with a particular name).
'around' indicates putting letters inside.
'america' becomes 'a' (common abbreviation - e.g. in organisation names).
'dub' placed around 'a' is 'DAUB'.
(Other definitions for daub that I've seen before include "Smear; bad painting" , "Coat with plaster" , "Do graffiti" , "Smear carelessly" , "Smear; plaster" .)