This is not a function of Google Places. These are called Place labels and they are set algorithmically. Having your Places verified helps but doesn't guarantee it. This is from Google: 

Having

The place labels shown on Google Maps are determined algorithmically based on a large number of factors, so there is no way to guarantee placement of your business on the map as a place label. One factor these algorithms consider is the accuracy of the business listing and the richness of the content associated with the listing, so you can improve the chances that your business will receive a place label if you claim it in Google Places.

Best

I was going to leave this lie and I already thumbed up Gianluca for his (as always) excellent response, but whenever I see the word spinning it bugs me. There was another question today re finding duplicate content on your own website. I went to copyscape.com and put in a portion of an article I had written about a drug in about October of 2010. I was looking to see if it showed up in two client websites as a blog posting. Imagine when I saw it in several other sites with poor grammar added and misused modifiers, etc.

So, the whole idea of using some crap spinning software and churning out anything in twenty different and bad permutations is the most counterproductive SEO tactic today. Then to submit it to clowns who are going to have links to you for a fee is the second most counterproductive.

Lastly, in SEO, when you have found the easy way to do something, generally, it is wrong or at best very temporary. Think about it, if it is easy every clown who professes SEO knowledge is doing it so there is no advantage. Those who truly work at SEO are the ones who succeed for themselves, their companies, and their clients. Write good content. Do the work to get good links. Then sit back and smile when you smoke these chumps.

Sorry for the rant. I had a moment

One thing here is more around copyright, etc. I was assuming the content you were transferring to Chinese was from a site your client had or you had. If that is so, it is not a problem.

If, by menu name, you mean title tag, it is important. If you mean you have a menu with a Main Tab = Cars and below that are several choices: Expensive Rental Cars, Moderate Rental Cars, Cheap Rental Cars, the main tab being cars will not hurt you. 
Look at the url  :  YourSite.com/cars/cheap-rental-cars

If that is how it looks, I see no problem with it. If it looks like this YourSite.com/cars and the thing you want to rank for on the page is cheap-rental-cars that by itself will not help but won't kill you. I would use the cheap-rental-cars and have a title tag that says Cheap Rental Cars | YourSite.com.

Hope this helped you out.

Andy

There won't be any problem as it is a different language. Even if you were doing it in Google, there is no problem with duplicate content in two different languages. Otherwise we would have to use totally different content on English/Spanish sites in TX.

iNet,

In answer to number 1, there is one giant in China and that is Baidu. Luckily,there are a lot of articles on SEO and Baidu (here is one 8 tips on Baidu and SEO). Also, there are articles on Search Engine Land, etc. so you should be good to go there.

As to number two and three, since I have no direct experience, I would have to refer you to the above.

We are handling a couple of sites in South America and working on an African site. The one cautionary would be that the only way to work with another language is to have a true language pro. So, you have to have someone who works professionally with translation of Chinese for mainland China on a regular basis. I would personally look for someone who has lived there or lives there now that already has clients or a body of work.

Sounds quite exciting, good luck.