Key Bank has a prepaid Mastercard they call "Key Possibilities". You can buy it at their banks for whatever denomination from $25 to $2500 you wish. The service fee for purchasing the card is $3.95.
I have bought them at times for online purchases where I'd prefer the vendor didn't have my regular credit card number. I've never had one denied by a vendor yet. When the amount gets down to an unusable amount, I take it to Key Bank and request a cash advance on it of one dollar less than the amount left on it. The charge for a cash advance on it is $1.00. That evens it out.
It is important to maintain an accurate record of it's balance, since there are no statements. The lack of statements is also a disadvantage because you can't monitor what was charged against it, or if the vendor followed through properly. Technically, the vendor could even double charge you, and you wouldn't realize you'd been ripped off until the card lost it's value prematurely. If you used the card for that purpose, you'd want to buy in values you're willing to risk losing.
When using it, it doesn't really matter what name, address or zip code you give. The name on those I get is just "Key Bank Customer". They're designed to give to others, so the address doesn't matter.
It has some disadvantages over regular credit cards, but for it's purpose it serves well.
Since I've never purchased them as gifts, I don't know if they have a "activation when received" feature. Without that, I can't see any more safety in sending it through the mails than sending straight cash.