Do we have any naam-kirtan of god Shiva similar to the Hare Krishna for Sri Krishna, in the shastras?
First of all, the "Hare Krishna" is a Mantra and not a Kīrtana, and the greatest Mahā-Mantra as per the Gauḍīya Vaiṣṇava's.
Now, Shiva Purana defines what is meant by a Kīrtana, as follows -
Verse 1.4.3, Shiva Purana
गीतात्मना श्रुतिपदेन च भाषया वा शंभुप्रतापगुणरूपविलासनाम्नाम् । वाचा स्फुटं तु रसवत्स्तवनं यदस्य तत्कीर्तनं भवति साधनमत्र मध्यम् ॥ ३ ॥
- By Kīrtana (glorification) is meant the clear expression of Śiva’s exploits, attributes, forms, sports, names etc. in good taste by reciting traditional lore, singing songs of praise even in mother tongue. It is the middle one of the three means.
So basically, anything that sings or talks about the glory, significance, or importance of God Shiva and his name, will constitute as an act of Shiva-Kīrtana, and even mother tongue is allowed in the Kīrtana.
As such there can be several songs and other forms of glorification in various languages for Shiva. For instance, the famous Hindi Aarti - Jai Shiva Omkara and, other song-playlist like this playlist - Holy Chants On Shiva & Shakti