Auto Assign User to Node
You can create a simple module, implementing hook_form_alter, add additional form submit action which checks the submitted values on your form, looks up if there is node matching them and finally loads and updates the node accordingly.

Alternatively, you can add the Existing Club Name field to registration, implement hook_user_insert, and do the same logic as described above. This would save you unnecessary web form and improve the user experience greatly.

EDIT:
Now that I think of it, it might be possible to achieve this using Rules module (https://drupal.org/project/rules) without coding. You add the field to the registration, create a rule, on event when user is created. Then iterate over all nodes of the Club content type (this should be possible with rules) and do a string comparison on each, to find the corresponding club. If the string comparison matches, you can easily change the node author. Please note that this solution is rather slow (and definitely not "right"), users could experience slow registration times.

Alternatively, you could change the rule event from user registration to form submission (which you have already) and therefore this (possibly) slow processing would not affect all users.

Also, I havent tried it, it's just an idea, but you should definitely try it.