What is the Apple / OS X name for "Alternate Data Streams"?
Apple uses "multiple fork" or the shortened form "multi-fork" consistently through its documentation, so it seems it is the official term. I list here a few examples:

https://developer.apple.com/library/mac/#documentation/General/Conceptual/SLGlobalGlossary/Glossary/Glossary.html (Last updated: 2010-07-09)


  HFS+  Hierarchical File System Plus. The Mac OS Extended file-system
  format. This format adds support for filenames longer than 31
  characters, Unicode representation of file and directory names, and
  efficient operation on very large disks. HFS+ is a multiple-fork
  volume format.


https://developer.apple.com/library/mac/#documentation/Porting/Conceptual/PortingUnix/io_porting/io_porting.html (Last updated: 2012-06-11)


  (...) some Mac applications also take advantage of the HFS+ file
  system’s ability to handle multi-forked files.


https://developer.apple.com/library/ios/#documentation/CoreFoundation/Conceptual/CFBundles/AboutBundles/AboutBundles.html (Last updated: 2010-07-08)


  Bundles can reside on volumes of many different formats, including
  multiple fork formats like HFS, HFS+, and AFP, and single-fork formats
  like UFS, SMB, and NFS.


When talking about "fork" in computing I can only think of either HFS+/HFS forks or the system call for creating a child process.