Can someone take back a transferred domain name?

No (with qualifications), once a Domain is transferred it cannot be transferred again for a period of 60 days. Also, a transfer requires a valid EPP key (Extensible Provisioning Protocol) something you explicitly have to give to them. Under most circumstances, a transfer can't take place without a valid EPP.

Qualifications are in regards to fraudulent or criminal events. From here (http://www.icann.org/en/transfers/policy-12jul04.h... :

In the event that a Transfer Contact listed in the Whois has not confirmed their request to transfer with the Registrar of Record and the Registrar of Record has not explicitly denied the transfer request, the default action will be that the Registrar of Record must allow the transfer to proceed.

Upon denying a transfer request for any of the following reasons, the Registrar of Record must provide the Registered Name Holder and the potential Gaining Registrar with the reason for denial. The Registrar of Record may deny a transfer request only in the following specific instances:

1. Evidence of fraud

2. UDRP action

3. Court order by a court of competent jurisdiction

4. Reasonable dispute over the identity of the Registered Name Holder or Administrative Contact

5. No payment for previous registration period (including credit card charge-backs) if the domain name is past its expiration date or for previous or current registration periods if the domain name has not yet expired. In all such cases, however, the domain name must be put into "Registrar Hold" status by the Registrar of Record prior to the denial of transfer.

6. Express written objection to the transfer from the Transfer Contact. (e.g. - email, fax, paper document or other processes by which the Transfer Contact has expressly and voluntarily objected through opt-in means)

7. A domain name was already in “lock status” provided that the Registrar provides a readily accessible and reasonable means for the Registered Name Holder to remove the lock status.

8. A domain name is in the first 60 days of an initial registration period.

9. A domain name is within 60 days (or a lesser period to be determined) after being transferred (apart from being transferred back to the original Registrar in cases where both Registrars so agree and/or where a decision in the dispute resolution process so directs).

Instances when the requested change of Registrar may not be denied include, but are not limited to:

* Nonpayment for a pending or future registration period

* No response from the Registered Name Holder or Administrative Contact.

* Domain name in Registrar Lock Status, unless the Registered Name Holder is provided with the reasonable opportunity and ability to unlock the domain name prior to the Transfer Request.

* Domain name registration period time constraints, other than during the first 60 days of initial registration or during the first 60 days after a registrar transfer.

* General payment defaults between Registrar and business partners / affiliates in cases where the Registered Name Holder for the domain in question has paid for the registration.

As soon as you are registered as the owner and you have entered your name servers, no.