The most common and most likely answer to this crossword clue is the 5 plus 4 letter word STAGE NAME
I've seen this crossword clue in The Sunday Telegraph
S
T
A
G
E
N
A
M
E
More clues leading to the result STAGE NAME
- Identity assumed for men, woman and me
- Contrary chap, say, probing food item on a bill?
- Upset agent with same soubriquet
- Get seaman excited with Lady Gaga?
- It’s assumed by performer, ditto when devious agent’s involved
- Manage set flamboyantly for Lady Gaga, say
- Dizzy agent blocking similar soubriquet
- Elton John, for example, gets a rousing hand back East
- Same agent used for Liberace, say
Buddy explains!

The straight part
We know that "Liberace, say" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case liberace, say = stage name.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.