If every King of England down to Richard III (d. 1485) was a direct male descendant of the counts of Anjou, why do historians arbitrarily stop calling this lineage "Anjou" or "Angevin" after 1154 and start calling it "Plantagenet?" And why is there another switch in names to "Lancaster" and "York" when the Angevin male line seems to be unbroken?
From what I'd gathered, 1154 is when historians start calling the English kings Angevins or the House of Anjou. Before that they generally refer to the House of Normandy (though some count Stephen separately as the House of Blois).
The switch from "Anjou" to "Plantagenet" is usually made between John and Henry III, as during his reign John lost control of the bulk of his French territories, including Anjou itself.
And why is there another switch in names to "Lancaster" and "York" when the Angevin male line seems to be unbroken?
To distinguish the competing lines, and out of a recognition that the main patrilineal line had failed and was now depending on the competing claims of cousins of the old line. Similarly, historians of the French monarchy generally distinguish between the Houses of Capet (Hugh Capet to Charles IV), Valois (Philip VI to Henry III), Bourbon (Henry IV to Charles X) and Orléans (Louis-Philippe), despite the fact that all of them descend patrilineally from Hugh Capet, and the Orléans were originally just a branch of the Bourbons.
"Plantagenet" comes from the Latin for the common broom plant, "planta genista", which was used by Geoffrey of Anjou (father of Henry II) as an heraldic emblem. it wasn't used as a dynastic name until the 15th century, after which it was retroactively applied to all of the English kings back to 1154.
the houses of Lancaster and York are named respectively for the descendants of John of Gaunt, 1st Duke of Lancaster, the third son of Edward III, and Edmund of Langley, 1st Duke of York, the fourth son of Edward III.