When speaking of the serialization process in general it never occurred to me (and I can't recall anyone else doing it either) to specify both the tasks of serializing and deserializing, unless there is a real necessity to do so. The latter is just implicit in the more general term we known as Serialization and that we use in common language.
So, were I to have a need to merge both read and write operations for the purposes of serialization and deserialization, I wouldn't think twice calling it Serialize or some form of it. Searching for some other word seems to me confusing, not to the point and a unnecessary exercise. IO and or ReadWrite seems convenient too, especially if the merged functions referred to the strict actions of reading and writting data to a medium. But Transduce? Literate?... Exchange? Really, enough joking.
As for mapping, MK27 is correct in my option. There's not requirement for serialization to perform any sort of data transformations. For all purposes, one can serialize an object by simply writing its current memory representation byte by byte. If there's any data mapping occurring, it will be a decision of the programmer usually to store it in a more convenient format for quick retrieval later or to be accessible by other programs. But definitely not anything deemed necessary to perform the task of serializing an object.
