It's honestly a really messy process to get (and keep) credit card processing. Most of us that have it have done so through creating a separate business entity, like a consulting business, and processing that way. I'm not listing my business as "Erin Black", so when you get a cc bill, itll just say "some consulting business, LLC."
Those of us who take other forms of payment outside of cash will let you know via our sites, normally in FAQs. Cash is always king, and if you don't see information about alternative forms of payment, I wouldn't ask. A lot of us also only offer regulars/trusted clients the option to pay electronically due to being charged back.
If you don't want someone to have your cc info and want to pay electronically, you can also do that via wire transfer, but that's horribly inconvenient for both you and the provider.
Every business that processes your credit card has some information about you on file, so I don't know what you mean by "financial information".
You could also just use a peer to peer payment app like CashApp, or Venmo. Some providers will also take Zelle as well, though that one is pretty limited. We get banned pretty frequently from these apps and from cc processing services though, so your best bet is to just take a cash advance from your credit card and pay in cash.
