Although the York and Lancaster's are considered "cadet branches" of the Plantagenet's they are as much Plantagenet's as the main line, they were both directly related to Edward III, and if they had surnames in those days and it was Plantagenet then it would be Plantagenet. It must be remembered that the name Plantagenet wasn't used until Richard of York, the father of Edward IV, started using the name as a way of subtly emphasizing his claim to the throne, and he hadn't murdered anyone, yet.
By the end of the war of the roses the 2 had wiped out just about every legitimate claimant and Henry Tudors claim was via an illegitimate female line from John of Gaunt.