I'm not sure exactly what you're asking. Every debit card I've seen in the last 3 years has had the Visa or Mastercard logo on it and acts like a credit card, in that when you give the number to a vendor they treat it like a credit card for processing purposes, but the funds are drawn from your account.
There's no reason anyone needs to know that your card is in reality a debit card rather than a credit card.
I think dharding is right on here, unless you have some sort of debit card I've not heard of yet. As long as it has the Visa or Mastercard logo on it, it will act and perform as a regular credit card, so any host that accepts either will be able to accept your card.
Actually it depends on the merchant provider. I had a merchant provider for another business and while I could accept credit cards the provider would not process debit cards with the Visa or Mastercard logo. The provider was not a small provider. Basically it had to do with the software processing; they hadn't updated. Most should accept debit cards now, but you still might run across a web hosting provider using a merchant whose provider does not allow debit cards.