Lusitania kinda maps onto modern day Portugal which is why that was the latin name for the Kingdom.
No such thing.
Modern Portugal does correspond to roughly the western half of Lusitania and southern half of Gallaecia, but early Medieval Portugal corresponded exclusively to south Gallaecia, and it's inhabitants were just called Galicians.
Portugal was named after a Gallaecian city, which (arguably) could mean Port of Gallaecia (or just Port-Port).
By the High Medieval period Portugal expanded into what was west-Lusitania, but it still kept it's name originary in Gallaecia and people called the kingdom some variation of "Portugallia"
It was only the early modern period, during the first pieces of nationalist literature (this might come off as shocking to people who associate the rise of Nationalism with the 19th century due to a focus on central European affairs, expecially Italy, Austria and Germany, but it's worth keeping in mind that by the 16th century Portugal had a completely homogeneous population and the same exact borders for nearly 300 years, there was already a clear sense of national unity in both literature and political affairs) that the Portuguese looked back in history to try to define their origin myth and they chose the Lusitanians because it corresponded to the majority of their current (which is the same as the 16th century) borders as well as being the most famous and hyped pre-roman people of Hispania in the literature of the time.
So essentially the genesis of Portugal is in Gallaecia, and their early medieval identity was undistinguishable from Galicians, and only in the early modern period they began trying to associate themselves with Lusitanians.