You're asking for a dream scenario from 2010 - back then, it was still possible to set up your company with one of the many payment processors quite anonymously if you knew how to do it. Today, it requires so much more, as you can also read about in Mentor Group Gold if you're interested in this.
The simple answer is no, you cannot find any anonymous credit payment solution for your business in 2024 - it's forbidden, and due to all the insane regulations that have been and are coming into this market, it's not possible - a payment processor would receive a gigantic fine and possibly risk prison time depending on the severity of the issue in the company.