Well, no
Lusitania was the original name of the people that belong in the area
Hispania was Roman's forced name onto the area (probably, this is kinda disputed)
So, you're saying that Portuguese would name themselves Hispania or Spain in honor of the Romans
We're saying they would do Lusitania in honor of the Lusitanian's
Why would ours make more sense?
Because Portuguese is still considered to this day to be Lusophones
Even in modern day, the Portuguese are acknowledging Lusitania.
The Lusitanians only lived in a small portion of the Roman province of Lusitania, the fact that Portugal uses the term Lusitania is a clear example of reusing a Roman geographical term to refer to a later region, like Hispania (Spain) for the Castillian-Aragonese Union, Helvetia for Switzerland, Gaul for France, Britannia for Great Britain/UK and many others. So, it's clear reference to the Romans, since Lusitania was also forced by Romans onto the western part of the Iberian Peninsula.
The "to this day" argument is not really relevant here since we're taking about an alternate relaty that diverged many many centuries ago, before the difference between Spain , Hispania and Iberia was established. If Portugal had conquered the whole Iberian Peninsula, then Portugal would acknowledge Hispania. Similarly, if Castille and Aragon had never united, the term "Spain" would be vacant now, much like Iberia is.
Anyway, why changing the name to Lusitania after annexing the Peninsula? It would have encompassed that territory long before that point. I don't see any kind of correlation between those two things, formable nations or name changes should come after completing an objective. Why would be "Lusitania" locked until having conquered a far larger territory? You can form Great Britain after having control over a large part of said island, not all of Western Europe, for example.