There are check cashing places where you live; they sell prepaid reloadable debit cards. they give you a temporary card, and then you get a permanent one in the mail. Green dot doesn't work, except for Intertops when I tried it. But check out those branded by netspend.com. They should work. Order it on the net if you can't find a place in town that sells them (
www.netspend.com) In South Jersey you should be able to go into a check cashing store and get them. ALso see if you can get a VISA debit card on your bank checking account. If you can't consider opening up at another bank, especially a Credit Union. You will get a better deal on everything, interest, loans, fees, etc. etc. Walmart, grocery stores, drug stores all sell visa gift cards, but make sure they are good through out the world and are not green dot branded.
I don't think putting in the name of the bank is what gets it rejected. Putting in the name of the bank is something Greek asked you to do for security purposes. They make sure the name of the bank matches the name of the bank as registered in the database that VISA maintains.
Greek does not have agreements with banks, to pre screen out cards like this. If the error is the bank rejects gaming transactions, how would you know Greek is making htis decision based on what they know about the banks? My opinion they send it through, and an error code comes back. Just because it happens quickly doesn't mean Greek is making the decision.