Consistent naming, moved methods, etc.

There is a follow-up CL that moves code from this .cc to the private
part of the class in the .h file.

Bug: v8:9396
Change-Id: I9efac09baff7403bce1be9712c090d2ea70b60f6
Reviewed-on: https://chromium-review.googlesource.com/c/v8/v8/+/1748734Reviewed-by: Tobias Tebbi <tebbi@chromium.org>
Commit-Queue: Santiago Aboy Solanes <solanes@chromium.org>
Cr-Commit-Position: refs/heads/master@{#63203}