To be clear before we get into the companies. These are places to buy Bitcoin. Do not confused this with companies to hold your Bitcoin. In fact, I would highly recommend against holding your Bitcoin in any of these companies. These companies are all highly regulated as Money Service Businesses.
These companies would be watching your every transaction and recording it for all time. Nothing positive will ever come of this for you. Nothing negative may not ever come of it, but I can promise nothing positive will ever come. You might not even do anything wrong but their “compliance department” might find “irregularities” and then before you know your account is closed.
This has happened to many many people who’ve done nothing wrong and it is completely avoidable. Be smart and use these companies for only buying and selling Bitcoin. Once you get your Bitcoin, immediately transfer them to your outside wallet. Then make whatever transfers or purchases you want to do.
The wallet that you store your Bitcoin should never require your name, or any identifying information. There should be no KYC or AML involved. Ideally the wallet you store your Bitcoins should be only a wallet that does not partake in any other activities like deposits and withdrawals into fiat currencies.
One wallet that I have used is www.Blockchain.info. This is the most popular web wallet in the world for Bitcoin. The only required information is an email address. They don’t ask for your name and never ask for any identifiable information and don’t do any verification.
Blockchain.info doesn’t need to do these things because they are completely a wallet company only. They only transfer digital bits back and forth through the Internet. They never touch fiat currencies. To maintain the company, they sell advertising that you will see when using their wallet.
One thing to remember is that with all client side encryption programs like Blockchain.info if you lose your password, you totally and completely lose all your Bitcoins. There is no way to get them back.