The label "Angevin Empire" is a modern historiographic retronym, not a name contemporaries used. Historians disagree on whether it names a coherent political entity or is a convenient shorthand for what was really an assemblage of independent, sovereign territories (Normandy, Anjou, Aquitaine, England and others) bound only by their common ruler, with no shared institutions, law, or capital.
What would resolve this A clear scholarly consensus on whether the Plantagenet dominions had enough shared governance, institutions or self-identity to count as a single polity rather than a personal union; current historiography is split, with some scholars preferring "commonwealth" to "empire".
OpenMedieval European political historyWikipedia: Angevin Empire