If new users do not receive their new account credentials via emails with username & password you need to check first if you have enabled the option here:
Send Login Credentials
If this is checked, it could be that some other plugin or your theme overrides the “wp_new_user_notification” function. For example the ARMember plugin does this. To validate this you need to do a full text search on all plugins & your theme searching for this string “function wp_new_user_notification”. This needs to be removed.