Aegon the Conqueror never conquered Dorne, yet he was named King of the Rhoynar by the High Septon in Oldtown. The Rhoynar settled in Dorne when they fled Essos hundreds of years before Aegon's Landing. I know he meant to conquer Dorne, so I understand he calling himself their king before actually conquering them, but did he style himself king of the Rhoynar after he made peace with Dorne? I am also not sure if he was anointed by the High Septon before or after he made peace with Dorne.
Aegon styled himself as King of the Rhoynar from the beginning because he believed he would eventually conquer Dorne. This is similar to his use of the title 'Lord of the Seven Kingdoms even though he had only conquered six.From the Game of Thrones wiki:
all of the Targaryen kings starting with Aegon I himself styled themselves as "King of the Andals, the Rhoynar, and the First Men" and "Lord of the Seven Kingdoms" - despite the fact that Dorne remained independent. Aegon I had declared himself king of all of Westeros just before his army even landed on the continent, Dorne included. While Dorne had been able to resist his armies and dragons through guerrilla warfare, Aegon himself never acknowledged that this was a permanent state of affairs. Aegon and all of his heirs considered themselves the de jure kings of the Rhoynar and of Dorne, even if they had no de facto control over it (comparable to how medieval English kings would at times hold titles of lordship over "Wales", "Ireland", and "France", despite not controlling all or even most of these territories).