We say in the “Al Ha-Nissim” addition to prayers that the lead player in the Hanukah story was Matisyahu ben Yohanan the High Priest. The question is whether this Yohanan, Matisyahu’s father, was the famous Yohanan the High Priest or not. It is not entirely clear whether the term High Priest is going on Yohanan or Matisyahu. And even if it is going on Yohanan, it is unclear whether he is the Yohanan the High Priest mentioned in the Talmud, who served for 80 years and became a Sadducee at the end of his life.
There are three positions on the identity of the famous Yohanan the High Priest:
1. The Rambam (Introduction to Commentary to the Mishnah) and Roke’ah (Hilkhos Hanukah) are of the view that he was the son of Matisyahu, of Hanukah fame, evidently named after his own grandfather.
2. Sefer Yuhasin (1:16) and Seder Ha-Doros (2:Yohanan Kohen Gadol) state that Yohanan the High Priest was Matisyahu’s father and is the one mentioned in the “Al Ha-Nissim.”
3. Later scholars, including Doros Ha-Rishonim (part 2 p. 442) and Toledos Tanna’im Ve-Amora’im (vol. 2 p. 688), are of the view that Yohanan the High Priest was the grandson of Matisyahu and the son of Shimon.
R. Matis Kantor, in his THe Jewish Time Line Encyclopedia, has an interesting appendix on this subject.