The most common and most likely answer to this crossword clue is the 3 plus 8 plus 8 letter word THE TEARDROP EXPLODES
I've seen this crossword clue in Independent
T
H
E
T
E
A
R
D
R
O
P
E
X
P
L
O
D
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S
Buddy explains!
The straight part
We know that "Reward band name" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case reward band name = the teardrop explodes.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.