The answer is Yes. But depending on whether you have the proper expertise and equipment.
The rules and format for domain registration are quite specific and certainly complex in all their permutations.
With enough attention you could learn the procedures by yourself. However, the main stumbling block to registering for most people is the requirement that you must have name server computers set up to respond to the domain name for routing.
This refers to the Domain Name Servers (DNS) located all over the Internet which perform the translation back and forth between domain names and their numeric equivalents, called IP (Internet Protocol) addresses.
Without this equipment and capability, the domain name will not be registered.