Yes, it is possible to trademark a domain name so long as it is used in the same way all trademarks must be used, as an indicator of source and to distinguish your goods or services from your competitors. This means that it cannot be used solely as a domain name to access a website. It is important to note that just because you have a trademark it does not mean you are entitled to use that domain name. Someone may already own it and if that is the case then the only way to obtain it is to purchase it from the owner. The similarity of domain names can be taken into account when determining whether there is a likelihood of confusion with another trademark. In addition, using a registered trademark in a domain name be considered dilution. Such cases are generally resolved through the Anticybersquating Consumer Protection Act or the Uniform Domain Name Dispute Resolution Policy (UDRP). It is important to know your rights both as an owner of a trademark and owner of a domain name.
This blog is not legal advice and is not specific to your application. You should always consult an attorney.