How do I dissolve a publishing company that I created through ASCAP?

It sounds like you registered yourself as the publisher. There is nothing to dissolve. If you had a sole proprietorship you would/should have used an EIN and not your SSN. Just go to the FAQ section on ASCAP's website for steps for removing the publisher listed on any song. Contact an attorney to assist you with forming a publushing company.

Through ASCAP. If you also created a fictitious business name for this publishing company, you do that with your county's recorder.

Like the other attorneys, I'm not sure exactly what you mean by "dissolve a publishing company you created through ASCAP." You didn't really create a company through ASCAP. You created a publishing company (by giving it a name) and then had it join ASCAP as a publisher so that it could file songs and collect royalties. You've received advice on how to end a business so I'm adding another guess in on the ASCAP membership. If you want to end your publishing membership with ASCAP, you can do so. The easiest way to get more information would be to just call ASCAP and speak with someone about your specific membership. I've provided a link to the page where ASCAP provides information about your agreement with them as well as how to end it.