Most of cloud providers trust their New users using a combination of at least 2 methods: 1) Acount activation via valid email address 2)Biometric humain challenge (reproduce a manuscrit; response, execute simple addition, etcc..). But for old and valid existing users you can think (for a more security) to implement a zero-Knowledge proof challenge for example.

In timesof 10 minute eMail accounts, trusting an valid eMail Account does not help - at least you have to extend validation about hours. Some providers uses white list for eMail domains there an account is coupled with real personal identification, amazon is using that and also web.de But if you are not using passport copies or post ident, you will stay on the level of assumptions.

Earlier Web.de (email service provider in Germany) and eBay as well, sends activation code via post to home address. It’s pretty good but this will imitate the quality of the services. I believe mobile no will be more practical as What’s app and Viber do right now.

Provider can provide verification challenges:

1- validating e-mail accounts

2- verifying billing address ( if the cloud service intersects with a commercial purpose)

3- validating via phone number

4- Using something like google captcha to verify user is actually a human not an automated script to take down the cloud service.

5- Compound or two step verification can be used.

6- cyber laws (according to region) can also be stated to encourage users toward legal usage.

follow the site cloud security alliance.

you can use user behavior profiling and decoy technique  

What Alkhuder said resume what you can do right now to "trust" a user to any given service (Cloud computing included). Just be careful, as said by Mexner when considering e-mail validation, avoid any free service that are not reliable (10 minutes e-mail, for instance). 

Now, Swant suggested a way to keep that trusting. Indeed, a account can be compromised but not just that, most of those information can be forged, so you can give real information stoled from a target (name, address, credit card and billing information) and give an valid e-mail and phone number, but not related with those information. That way you can answer all the challenges and create a valid account to exploit "anonymously"  at least, for the hacker. Ok, I'm talking about a few cases here, for most of the users this will be enough to avoid any trouble or abuse from them.

But we must no forget the Pareto Principle, or 80–20 rule: 80% of the effects come from 20% of the causes.

So behavior profiling is a good idea to improve that trusting. The problem, profiling only works when considering the normal use against any activity that goes out of that! That's why Sawant also suggested decoy techniques! Brilliant! But you need to now your user bases and how to put those decoys to identify any unusual activity. Depending on what you want to observe, honeypots are great! You should also consider an IDS (I'm giving some links regarding IDS on Cloud bellow).

Trust is something you must earn and keep, it's a continuous process. And I almost forget one important thing: You must follow a police, what you will do when you found a account violating your terms of use? Ban forever after an investigation? Just block it? Inform the authorities? I would say we must rely on the cyber laws, as said by Alkhuder, and that depends according to each region/country. 

Well, enough for now. 

Cheers,

http://en.wikipedia.org/wiki/Honeynet_Project

https://awsmedia.s3.amazonaws.com/SEC402.pdf

http://www.sersc.org/journals/IJAST/vol34/8.pdf

My question is ,How the cloud provider trust their new  user and also what are the factors he considered for trusting ?