As I discuss in my answer here, Shiva is the name taken from Samhita of Vedas.
Here is 4.5.8 of Taittariya Samhita stating the name Shiva.
Here is 16.49 of Vajasena Samhita stating the name Shiva.
As from above image
is used there.
is used. Which is pronounced as 'Sh'.
Hence the correct pronounciation is Shiva.
Here 'a' is not long. If you pronounce with long 'a' ie. 'Shivaa' then it refers to consort of Shiva ie. Uma/Shakti.
However for the purpose of Devotional chanting, it doesn't matter whether you chant 'Shiva' or 'Siva' because in devotional chanting God sees our intention and devotion not our pronounciation.
For eg. Ramcharitmanas is a devotional masterpiece. There Tulsidas uses the name like 'Lakhan' for 'Laxmana', 'Siya' for 'Sita' and so on. Also in Hanuman Chalisa composed by Tulsidas:
Sukshma rupa dhari Siyahi dikhawa
(You showed your minute form to Sita
Laaye Sajivana Lakhana Jiyaye
(Bringing Sanjivani you Saved Lakshmana)
Thus pronounciation doesn't matter so much in devotional chanting. But it is better to pronounce in correct way. One needs extremely precise pronounciation while chanting Veda Samhitas only.