Consider adding either of those modules (quotes are from their project pages):
Honeypot uses both the honeypot and timestamp methods of deterring spam bots from completing forms on a Drupal site. These methods are effective against many spam bots, and are not as intrusive as CAPTCHAs or other methods which punish the user.
Invisible antispam without CAPTCHA, questions, puzzles, counting animals, math and etc. Just install and forget.
CleanTalk is a SaaS spam protection service for Web-sites.
CleanTalk uses protection methods which are invisible for site visitors.
Using CleanTalk eliminates needs in CAPTCHA, questions and answers, and other methods of protection, complicating the exchange of information on the site.
BOTCHA Spam Prevention is a highly configurable non-CAPTCHA spam protection framework.
BOTCHA, doesn't abuse human users, BOTCHA protection is completely
transparent to them and non-intrusive.
If these modules still don't help to reduce your issues, then I would go for plan-b, i.e:
- consider reviewing (extending if needed) your registration form, by adding 1 (or more) field(s) so that it becomes AbitMORE difficult to complete registration requests. Either some obvious question for which your target audience should know the answer by heart, or something for which the answer can be found by first browsing around on your site. Yet another option is to ask some question about their real name or address, which may help later on how "serious" the request is.
- make admin approval required for every new user registration request. This will reduce the speed of "registered" users to the speed of an admin approving / reviewing such requests.
Pretty sure this plan-b will help a lot ... up to you to decide if it fits with "the entire point of your site".