How i get the All Android Application categories name?

Application categories correspond to a classification in Android Market, but not something you can check on the application itself. What you can do is to query the Android Market for information of a specific application.

Android Market identifies applications by package name. So get an ApplicationInfo for the package you want to query about (check PackageManager documentation) and use ApplicationInfo.packageName.

Then query Android Market about the package name you just got. Here's a non-official API http://code.google.com/p/android-market-api/

Hope it helps.

Create a raw JSON POST request, with an array of the packages you want to categorize:

{
  "packages": [
    "com.pixmix.mobileapp",
    "snooze.ninja"
  ]
}

Send it to:

http://api.wheredatapp.com/data

And here's the response:

{
    "apps": [
        {
            "category": "Photography",
            "created": 1430868349,
            "package": "com.pixmix.mobileapp"
        },
        {
            "category": "Productivity",
            "created": 1427510152,
            "package": "snooze.ninja"
        }
    ]
}