I am getting texts pretty frequently about my apple ID verification code and I haven't had an Apple ID in almost a year. I'd still like to keep it secure and wondering how I can prevent this

Since you have 2 Factor Authentication enabled on the account, unless someone can access one of your trusted devices, the account is secure. If you want to try to stop the messages, you can do a name change on your Apple ID account.

Note the restrictions in the article.

Apple ID Name Change

 What to do after you change your Apple ID or password - Apple Support     I suggest doing this before you change your Apple ID or password.