The other Borg get names like 4th of 12, adjunct matrix blah blah. So why did Captain Picard get a name when he was assimilated, instead of a numerical code / designation like all the other drones?
Giving him a name would make it easier for him to perform his primary function as an intermediary in the assimilation of Earth, giving him a slightly more human quality than other Borg had:
The Borg intended to use Picard as an intermediary, a spokesman for the Human race in order to facilitate the assimilation of Earth in order to make the process as quick and efficient (or as perfect, if you keep the Borg's driving force in mind) as possible with the fewest number of casualties on both sides.
It was later revealed that the Borg Queen herself was onboard the cube to oversee Picard's assimilation into Locutus. She had intended for Picard to become her equal counterpart, but when Picard refused to give himself willingly and accept his assimilation, the Queen was forced to turn Locutus into just another drone.
I guess being the Queen's consort entitles you to more than just a number.
Locutus is not a name, it is his function. "Locutus" came from Latin and means "the one who speaks" like in the word locutor.
Picard was not Locutus of Borg, he is more like the Locutus of Borg, but the Locutus could be anyone else. They choose Picard to do that because he was the "locutus" of the Enterprise on their first encounter.