Namaskaaram..

It seems Shiv Puranam states/lists baout 19 incarnations/partial incarnations of Lord Shiva

1. Piplaad Born to sage Dadhichi & Suvarchas; his story teaches that even fate written by Brahma can be challenged through devotion to Shiva                                           
2. NandiThe divine bull; gatekeeper of Kailash and Shiva’s most devoted attendant — considered a full Shaiva avatar
3. VeerbhadraThe immensely fierce form Shiva created from his matted locks to destroy Daksha’s yajna and avenge Sati’s death
4. BhairavaThe terrifying form that arose when Shiva clipped one of Brahma’s five heads — also the guardian of all Shakti Peethas
5. AshwatthamaThe Kuru warrior born carrying Rudra’s portion; immortal Chiranjivi still wandering earth
6. SharabhaHalf-lion, half-bird (8-legged) ferocious form during Narasimha avatar
7. GrihapatiBorn as the son of sage Vishwanar and Shuchismati in response to their deep tapas; taught the path of a householder-devotee
8. DurvasaThe famously short-tempered sage — son of Atri and Anasuya — known for powerful curses and boons; embodied Shiva’s Rudra temperament
9. HanumanBorn to Anjana through the grace of Vayu; the Shiva Purana explicitly calls him a Rudravatar — Shiva’s 11th Rudra form incarnate
10. RishabhaThe great ascetic king; father of 100 sons including Bharata (after whom India is named); also honored in Jain tradition as the first Tirthankara
11. Pippalada (second form)Some recensions list a second Pippalada manifestation distinct from #1 — a great teacher of the Prashna Upanishad
12. YakshaThe mysterious Yaksha form Shiva took after the Devas slew demon Vritra and became arrogant — he humbled Indra, Agni & Vayu by appearing as an unknowable being (also referenced in Kena Upanishad)
13. KirataThe hunter disguise Shiva took in the forests of Indrakila to test Arjuna — fought him and was pleased by his valor; granted him the Pashupatastra
14. AvadhutaA wandering, naked, unattached form of Shiva who appeared before Indra to teach him the lesson of humility and non-attachment
15. Bhikshu (Brahmachari)The wandering mendicant/celibate student form Shiva took to test Parvati’s devotion and sincerity before accepting her as his consort
16. SureshwarA form taken specifically to grant liberation to the devoted boy Upamanyu, who performed severe tapas for Shiva’s grace
17. Brahmachari (Siddha form)Some texts list a distinct Siddha-Brahmachari form that appeared to the Saptarishis (seven sages) to teach the highest Shaiva philosophy
18. Sunartaka (Nataraja form)The cosmic dancer form — while Nataraja is often seen as a permanent form, some Purana recensions count the specific manifestation of Shiva as a divine dancer before the sages of Daruvana as a distinct avatar
19. YatinathA wandering ascetic (yati) form Shiva took to test the hospitality and devotion of a tribal devotee named Aahuk and his wife — they gave up their lives for the guest, and Shiva blessed them

adiyen