In the preface to The Plantagenets: Warrior Kings and Queens who made England, Dan Jones states that the Plantagenets ruled from Henry the II to Richard II's deposition by Henry Bolingbroke (Henry IV). But afaik, Henry IV and Richard II were both descended from Edward III who himself descended from King John and, consequently, Henry II. So why is Richard II considered the last plantagenet king when both him and Henry IV had the same blood?
Is it more of a territory-ruled question? Did the name depend on also controlling Anjou?
Quite simply, he often is. I remember watching Dan Jones's TV series that the book was a companion to. I also sort of disagreed with him calling the death of Richard II the end of the dynasty (in fact I wouldn't be surprised if he disagrees with this himself). Jones pretty quickly followed up with a series on the Wars of the Roses and an accompanying book, The Hollow Crown. So in actual fact he did cover the dynasty until Richard III, just in separate parts. The name certainly didn't depend on controlling Anjou; no English king had ruled Anjou since John. That's partly why Henry II, Richard I and John are called the 'Angevin kings'.
Usually, dynasties are taken to mean unbroken male lines. However, there is some precedent for seeing male-line cadet branches of a house as a break, such as referring to the House of Valois separately from the House of Capet. The Houses of Lancaster and York were both cadet branches. There may be some element of Tudor legitimisation going on here - if you see the 15th century kings as being from the Houses of Lancaster and York, and not Plantagenet, then the Tudors don't represent such a break with continuity.
Ironically, no Plantagenet actually used it as a personal surname until Richard, Duke of York, the one who started the Wars of the Roses. This was to emphasise his royal descent. However, York's claim to the throne came from the female line of Edward III's second son, not from his paternal descent from Edward III's fourth son. So this complicates things more - even though the Yorkists are male-line Plantagenets, their claim doesn't come from the male line.
It's also a matter of convenient historical labels. The Houses of Lancaster and York were certainly separate families, and they also sort of represent two distinct regimes. Between Henry IV and Henry VI there was some level of continuity of government and this came to an end when Edward IV took over.