How to debug user_register hook

Rafael, (as requested, turning comments into answer)

‘user_register’ fires when a user registers, not when a user is edited or updated. Try something like https://codex.wordpress.org/edit_user_profile_update

Wrt output in hooks. It depends when/how the hook is being executed. The user profile ones are tricky because wp does stuff to prevent a double submission. One could use error_log to output where one can read it. More detail here: Debug output during filter execution doesn’t work

This might also help to understand https://stackoverflow.com/questions/7878279/… and for plugin specifc logging How to log plugin errors to plugin error_log file