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.
$f in the target pattern will be replaced by the full original filename. One could also use
$2, etc. to refer to any parenthesized capture groups in the source pattern (there are none used here as it's not needed).
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.