>
> Thanks, finally there is an option to avoid typing extra C-r.
>

:-)  And thanks for your feedback!

>
> Is it possible to find a clearer name?
> Maybe isearch-repeat-on-direction-change would be better with the prefix 
> 'isearch-repeat-' to hint that it applies to the commands 
> 'isearch-repeat-*'?
>

Done.

>
> This breaks the following feature:
>
> When isearch-forward is t:
> - C-1 C-r moves to the previous match (like your patch does without 'C-1')
> - C-2 C-r moves to the second previous match
> - C-u -1 C-r moves to the next match
> - C-u -2 C-r moves to the second next match
>
> This is due to these lines in isearch-repeat-backward:
>
>               ;; Reverse the direction back
>               (isearch-repeat 'backward))
>              (t
>               ;; Take into account one iteration to reverse direction
>               (when isearch-forward (setq count (1+ count)))
>
> When the new option is non-nil, there is no need to increment 'count'.
> Also the new option should be let-bound to nil around the call to
> '(isearch-repeat 'backward)' above to just change the direction back
> without moving to the next match.
>
> The same applies to isearch-repeat-forward and when isearch-forward is nil.
>

Fixed, thank you!