Design surrounding emblem is oddly vulgar (8)
I believe the answer is:
plebeian
'vulgar' is the definition.
(synonyms)
'design surrounding emblem is oddly' is the wordplay.
'design' becomes 'plan' (synonyms).
'surrounding' means one lot of letters goes inside another.
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
'emblem'+'is'='emblemis'
The alternate letters of 'emblemis' are 'ebei'.
'plan' going around 'ebei' is 'PLEBEIAN'.
(Other definitions for plebeian that I've seen before include "Lacking in refinement" , "Of the common people" , "Of the lower social classes, as in ancient Rome" , "Lower-class; commoner" , "not refined" .)