The phrase "apply the name" is correct and usable in written English.
You can use it when discussing the act of assigning or using a specific name for something.
Example: "In this context, we will apply the name 'Project Phoenix' to our new initiative."
Alternatives: "assign the name" or "use the name."
In 1892, that company decided to apply the name to a new line of canned peaches.
Several authoritative sources, however, frequently apply the name to the terciopelo (B. asper) and the common lancehead (B. atrox) of South America.
The name, which is derived from Pelopos Nisos (Island of Pelops, a legendary hero), does not appear in Homer, who preferred to apply the name of Árgos, a Mycenaean city-state, to the whole peninsula.
Some historians apply the name house of Anjou, or Angevin dynasty, to Henry II (who was also count of Anjou) and his 13 successors; other historians label only Henry II and his sons, Richard I and John, as the Angevin kings and, for want of a better name, label their successors, notably Edward I, Edward II, and Edward III, as Plantagenets.
Well, it would seem to be the property had by all and only the things to which we can properly apply the name 'George'.
For this reason, we do not apply the name "Agate Bridge Bed" to any Flattops One sandstones.
Even after a century, we should only apply the names of the honored dead to brand-new infrastructure.
Some surviving writings, however, indicate that contemporary writers may have applied the name to the harp.
Fortey, with more than 150 new trilobite names to his credit, applied the name monroeae (after Marilyn) to one with a singularly hourglass shape.
To this hypothetical substance Georg Ernst Stahl, at about the beginning of the 18th century, applied the name phlogiston (from Greek, meaning "burned").
Restaurants, takeout stands and drive-ins probably applied the name "burger" to their shrimp patties in the 1950's in the wake of the expanding McDonald's hamburger empire.
