The most common and most likely answer to this crossword clue is the 7 letter word NO-NAME
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More clues leading to the result NO-NAME
Buddy explains!

The straight part
We know that "Put otherwise, ‘anon’; also, dishearteningly, ‘mere’!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put otherwise, ‘anon’; also, dishearteningly, ‘mere’! = no-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.
What does NO-NAME mean?
NO-NAME noun- Someone or something lacking a recognizable name, identity, or reputation.
- Lacking a recognizable name, identity, or reputation; not noteworthy.