[ios] Expose ChromeBrowserState name

In preparation for referencing to ChromeBrowserState by name only
in ChromeBrowserStateManager and BrowserStateInfoCache, store the
ChromeBrowserState's name as a property and expose it publicly.

The method GetDebugName() returns the name and is renamed to
GetBrowserStateName() to make it clear that this method is not
limited to debug.

Bug: 336767700
Change-Id: I57516f621d44b72bc6b10289dcd93f004a28ad2a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5544733
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Commit-Queue: Sylvain Defresne <sdefresne@chromium.org>
Auto-Submit: Sylvain Defresne <sdefresne@chromium.org>
Reviewed-by: Federica Germinario <fedegermi@google.com>
Cr-Commit-Position: refs/heads/main@{#1322731}