Hi Krishna,
Renaming is perhaps a new trend. It is basically realigning Information Technology to serve the business. Ensuring/forcing application support and application developers learn/understand business rather than forcing business users to start learn/understand technology. It's like you said, who else does technology users work for?
Renaming Information Technology departments to Business Technology Departments makes it more sensible thereby developing a culture and habit for the technology users to be more associated with business users and talk their language, terminologies. Rather than technology users go to a meeting to collect the business requirements and start talking - we can integrate systems using SOA architecture, Java API, XML, blah blah and the business users go blistering barnacles...:)
On the other item you queried, (mix Business process and IT process), it possibly is not mixing; rather realigning IT processes that do not meet a business need. Obviously, there are quite a lot of IT processes that cannot be done without. However, the ultimate aim of an IT process should be to deliver a business need. If not, that IT process needs to be revisited and possibly made redundant as it shouldn't even exist.
Good luck...Nissar