A namesake is a person named after another, or more broadly, a thing (such as a company, place, ship, building, or concept) named after a person. According to the Oxford English Dictionary, a namesake is also defined as "a person or thing having the same name as another".
In general, the second recipient of a name, named for the first, is said to be the namesake of the first. The attribution can, however, go in the opposite direction, with namesake referring to the original holder of the name (the eponym).
Strictly speaking, a namesake is only a person named for another person—i.e., for the sake of the other's name, to keep it alive. Many dictionaries, however, following colloquial usage, acknowledge that things as well as persons may be or have namesakes, and (usually in a secondary definition) that the other for whom the person (or thing) is named, strictly the latter's eponym, may be called its "namesake".
Naming a child after a relative, friend, or well-known person is a common practice in the English-speaking world. When a son is named for his father, it is customary (primarily in the United States) to add "Jr.", "III'", or another name suffix to the name of the son (and sometimes "Sr." or a prior number to the father's name), in order to distinguish between individuals, especially if both father and son become famous, as in the case of poet Oliver Wendell Holmes Sr. and his son, Oliver Wendell Holmes Jr., an Associate Justice of the United States Supreme Court. Sometimes the "Jr." or "Sr." suffix is applied even when the child's legal name differs from that of the parent.
One notable example is that of the singer Hiram King Williams, known professionally as Hank Williams, and his son Randall Hank Williams, known professionally as Hank Williams Jr. Nothing prohibits girls named for their mothers from using similar suffixes, but no such tradition has become established. Notable is Thoroughbred jockey Rosemary Homeister Jr. whose mother was also a jockey before turning to training. A more archaic method of distinguishing father from son was to follow the name with the Elder or the Younger, respectively, e.g. William Pitt the Elder and William Pitt the Younger.
Among Ashkenazi Jews, it is customary to name a child after a dead parent (e.g., the child's grandparent), but never after a living person. Sephardic Jews traditionally are encouraged to name their children after relatives, living or dead. Greek families traditionally name a child after its paternal grandparents and the second child of the same sex is named after its maternal grandparents.
Buildings, such as the Trump Tower, and companies, like the Ford Motor Company, are often named for their founders or owners. Biologic species and celestial bodies are frequently named for their discoverers. Alternatively, their discoverers may name them in honor of others. Occasionally, material goods, such as toys or garments, may be named for persons closely associated with them in the public mind. The teddy bear, for example, was named for President Theodore "Teddy" Roosevelt, because of a popular story in which the then-President objected to cruel treatment of a bear by hunters.
The fedora hat may be considered the "namesake" of a fictional character, Princess Fédora Romanoff, from an 1887 play, Fédora, by Victorien Sardou. In her famous portrayal of that character, Sarah Bernhardt wore a soft felt hat with a center crease, which became known popularly as a "fedora".