@Randall
You will never stop all of them (they even appear on Stackideas occasionally) but you can reduce the number who get through by taking the following steps:
1. Install the SpambotCheck Joomla Plugin from vi-solutions. It is free and extremely efficient at blocking almost all spam registrations. It also allows you to see a logged list of spam attempts that were rejected with full details, so you know how often you are attacked.
2. Join BotScout and get an API key, essential if you are using a newletter component (for example AcyMailing, which is excellent).
3. Join Stop Forum Spam and get an API key, especially if you are using a newsletter component (AcyMailing allows you to activate BotScout and StopForumSpam)
4. If a subscriber gets through SpamBotCheck to 'register' as a new member on your site and you are not sure if they are spam, copy the email address and paste it into the StopForumSpam search box (you do not need to have an account to do this) and it will show a list of accounts used by the email if it is spam. You can do the same at BotScout, but I would use StopForumSpam first.
5. If you have an account at StopForumSpam and/or BotScout submit your spammer details to their website if not already on their list as it will help others block spam attacks.
6. Delete or block the IP (I prefer to delete once the record is on the StopForumSpam or BotScout list.
7. Use Recaptcha - it may not be as effective in blocking the more sophisticated spammmers, but every little helps.
8. Go to Joomla Global Configuration - Users Configuration and set New User Account Activation to 'Admin'. It means they need to verify their email and you (or whoever you designate to approve new registrations) must approve everything, but when starting a new site this is possibly the best way to control new members until the number of daily applications gets too big for you to manage, even with effective delegation. You can then change it to 'Self' for the applicant to confirm email address and auto register if they do, or 'None' if you want people just to register straight away (good luck with that option.........
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9. If they still get through and start posting crap, remove it, add their details to StopForumSpam and BotScout, then delete them.
I hope this helps Randall, I have Akeeba Admin Tools and CloudFlare with SiteGround but still followed the above and only about 1 or 2 get through, making it only a minor issue, not a major headache.