Trademarks are words, symbols or devices used to distinguish the goods or services of one business from those of
others. Throughout this article the word “mark” us used to mean both Trademarks and Service Marks; the difference is the type of basic use, either for goods or services. What I state for marks generally applies to both.

THE LAW: § 45 (15 U.S.C.. § 1127).

The term “trademark” includes any word, name, symbol, or device, or any combination thereof–
(1) used by a person, or (2) which a person has a bona fide intention to use in commerce and applies to register on the principal register established by this chapter, to identify and distinguish his or her goods, including a unique product, from those manufactured or sold by others and to indicate the source of the goods, even if that source is unknown.

Service mark. The term “service mark” means any word, name, symbol, or device, or any combination thereof–
(1) used by a person, or (2) which a person has a bona fide intention to use in commerce and applies to register on the principal register established by this chapter, to identify and distinguish the services of one person, including a unique service, from the services of others and to indicate the source of the services, even if that source is unknown.

To understand the above we also need the following:

Titles, character names, and other distinctive features of radio or television programs may be registered as service marks notwithstanding that they, or the programs, may advertise the goods of the sponsor.

The word “commerce” means all commerce which may lawfully be regulated by Congress.

The term “principal register” refers to the register provided for by sections 1051 to 1072 of this title, and the term “supplemental register” refers to the register provided for by sections 1091 to 1096 of this title.

Person, juristic person. The term “person” and any other word or term used to designate the applicant or other entitled to a benefit or privilege or rendered liable under the provisions of this Act includes a juristic person as well as a natural person. The term “juristic person” includes a firm, corporation, union, association, or other organization
capable of suing and being sued in a court of law.The term “person” also includes the United States, any agency or instrumentality thereof, or any individual, firm, or corporation acting for the United States and with the
authorization and consent of the United States. The United States, any agency or instrumentality thereof, and any individual, firm, or corporation acting for the United States and with the authorization and consent of the United States, shall be subject to the provisions of this chapter in the same manner and to the same extent as any nongovernmental entity. The term “person” also includes any State, any instrumentality of a State, and any officer or employee of a State or instrumentality of a State acting in his or her official capacity. Any State, and any such instrumentality, officer, or employee, shall be subject to the provisions of this chapter in the same manner
and to the same extent as any non-governmental entity.

Trade name, commercial name. The terms “trade name” and “commercial name” mean any name used by a person to identify his or her business or vocation.