As per Shiva Purana which 28 avatars of Shiva did he tell to Brahma? Also Shiva said the names of Sage Vyasa of each Mahayuga. What are those?
Chapter 4 and 5 of Satarudrasamhita of Shiva Purana describes the 28 Avatars of Shiva. Shiva takes these avatars at end of every Dvapara Yuga with Vyasa to teach Yoga techniques for people of Kali Yuga. He will have 4 disciples in each Yuga and these disciples teach the people of Kali Yuga and help them in liberation. These are the names of Avatars of Shiva in chronological order in this Vaivastara Manvnatara of Svetavaraha Kalpa.
- Sveta muni
- Rsabha (well known Avatar of Shiva)
- Laanguli Bheema
- Yogatma and becomes popular by name Lakuli.
Lakuli is identified as Lakulish who revived Pasupata Sect.
For different Vyasas, see this answer.
Note: Shiva Purana doesn't contain some names. So, those names are taken from Kurma Purana (Pg No- 333)