The procedure for registering a trade name varies a fair amount from jurisdiction to jurisdiction, but it is usually allowed. (law.stackexchange.com)
SELA and the SELA logo are trade / service marks and / or registered trade names of Sela Public Charter School (selapcs.org)
If you operate a business (without a legal entity such as a corporation or LLC), you generally have to register this trade name with a state or county government. (inc.com)