[Japan] Make alternative name types syncable

Recently the support for autofill stored alternative name types have
been added. The support for syncing them should be added.

Bug: 359768803
Change-Id: I2589c68b8e6af11dbfa447b9caa2d7949396019d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5975735
Reviewed-by: Florian Leimgruber <fleimgruber@google.com>
Auto-Submit: Karol Sygiet <sygiet@google.com>
Reviewed-by: Mahmoud Rashad <mmrashad@google.com>
Commit-Queue: Mahmoud Rashad <mmrashad@google.com>
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Cr-Commit-Position: refs/heads/main@{#1376401}