Stopping frequent 'iOS account breached' messages

Those are scam attempts. Do not interact with them.

While there really is no definite way to stop these scammers, I would suggest you filter messages from unknown senders, then they are filtered separately and you won’t be notified by them. Go to Settings > Apps > Messages > Message Filtering, then turn on Filter Unknown Senders.

Learn more:

Block, filter, and report messages on iPhone - Apple Support

Recognize and avoid social engineering schemes including phishing messages, phony support calls, and other scams - Apple Support

Prevention is the key. Once you give out your phone number or email address, it is being sold to the scammers. They spoof the sending number, so blocking them on your device has little benefit. If you have ever followed a link in a message, then it alerts the scammers that you may be susceptible to following their instructions, and that only means you will receive more of them. For SMS messages, most cell providers have Spam blocking available, and that is the best place to stop them from even being sent to your phone.

To help prevent exposing your email address, Apple has a service called Hide My Email, that allows you to create additional email addresses that can be used on third party sites, so your actual Apple ID used for Messages is not being used. This would be helpful for messages sent with iMessage to your account, but won't help with SMS messages.

What is Hide My Email? - Apple Support

There are apps available too, but I would not be the best source for any specific recommendation.

oldetooles wrote:

Every phone number that they come from is blocked immediately. They have to be coming from different senders because this has been going on for over 6 months 1-4X daily.

You should also try contacting your carrier as most they usually offer spam blocking services. Sometimes they are free and other times cost a small amount per month.