In the zsh shell, the following would rename the three files shown:
autoload -U zmv
zmv -v -- 'report<1-3>.txt' 'my$f'
The source pattern should be a valid zsh extended globbing pattern (quoted), and the source pattern used here simply matches the three filenames that you mentioned.
The $f in the target pattern will be replaced by the full original filename. One could also use $1, $2, etc. to refer to any parenthesized capture groups in the source pattern (there are none used here as it's not needed).
From the bash shell (passing the source and target patterns to the zsh -c shell as arguments):
zsh -c 'autoload -U zmv; zmv -v -- $1 $2' zsh 'report<1-3>.txt' 'my$f'
This answer ignores the issue of name collisions.