We shouldn't be tagging items with both google and some other tag like google-search or gmail. google should be used for the Google search engine. Use the specific app name for each app. Of course, multiple tags for multiple apps is fine.
Google should be treated like an application, not a company (unless the question is specifically about the company, which leads to a little confusion, but probably not too much). You wouldn't use a microsoft tag on an Excel question.
You can see from most of the cases in Super User how it should work, like so.