The processor that put you on the list can in some cases remove you from the list, if you manage to convince them that it was a genuine mistake that you have learned from and won't repeat. But knowing Stripe and seeing as it's been 3–4 years by now, it might not go anywhere. The good news is you're likely not going to be on the list for much longer. In a couple of years, the record is probably expunged.
In the meantime, you can only open your own merchant accounts without your name appearing as director, shareholder, user, or UBO.