I don't think there is "IANA naming function department" but there is "IANA functions department" So i propose the following:

The IANA naming functions, related administrative staff and resources, processes, data and know-how would be legally transferred into PTI from the exiting "IANA functions department"

MM: Not quite right. It is the entire IANA functions department, not just the naming-related parts of it, that would be transferred to PTI.

The IANA portion of the ICANN budget related to naming would be subject to.......

MM: Again, it makes no sense to keep the other parts of the IANA functions separate from the naming parts. The entire department must be legally separation.