Radhe Krishna,
A few corrections.
The name of lord shiva is clearly mentioned in Yajur Veda. In the middle of Shri Rudram you would find the verse "Nama Shivayacha".
Shri Veda Vyasa only compiled and divided the vedas for the purpose of proper implementation of the same in performance of yagyas. Every major yagya is performed with scholar from all the three vedas each one of them having separate roles in the performance of yagyas.
about a 100 shakas (Branches) of yajur veda only one is available now. of about 1000 shakas of sama veda only 3 is availablel now. about a 100 and odd shakas of rig veda only 1 is available now.
Veda vyasa did not compose the vedas but compiled them.
A clear study of vedas would reveal that not only shiva,
but Shiva, Vishnu, Ganesha, Surya, Shakthi all of them find repetitive references in vedas.
Regarding puranas - in Every purana, (puranas written as per purana lakshanas all of which should be available in every purana - one among them is shrishti varnana - how the universe and living beings are created) - there are details about the creation
All the puranas composed by veda vyasa who is an incarnation of lord vishnu.
It is said that
"Vyasaya vishnu roopaya vyasa rupaya vishnave"
From the puranas composed by Veda Vyasa - depending upon the purana one takes for interpretation - one can comfortably argue that Shiva or Vishnu or Ganesha or Surya or Shakthi or Even Skanda has created the world and all the deities including those other than the main deity of the purana.
In shiva purana it is shiva who has created everything including lord vishnu
In Vishnu Purana it is lord vishnu who has created eveerything including lord shiva
likewse it goes.
So who created whom is rather a matter of interpretation and depends upon the tool of interpretation.
In the very beginning, one friend unknowingly included even Bhagavath gita among puranas which is utterly wrong.
Radhe Krishna