Why does my iPhone not have iOS 16 even though I've updated?

iOS 16 won't be available to us normal users until sometime in the fall. When iOS is released, it will appear as an update on your phone.

I hv recently purchased i phone 13 pro

still my phone is on 15.5 version.

please update my phone to 16 version

Because iOS 16 was announced yesterday, but will not be released for several months.

I want to install my phone version

You can't.

iOS 16 has not been released yet. It is still in beta. It will be release to the public sometime around September of this year.