A "trade name" is the name under which a company conducts business, or by which its business, products, services are identified. It may or may not be registered as a trademark. An example of a trade name is Kleenex, which identifies a brand of tissues. See www.uspto.gov.
A "covenant" is a legal promise obligating a party to do something. Covenants are typically contained in contracts such as employment agreements, notes, loan agreements, and mortgages. For example, a mortgage could have a covenant that the borrower will undertake to make payments on the mortgage and to maintain the property.