Do your friends address you as "Shiv" or "The Shiv"?
The "name" of the United States is not actually a name. It is, instead, a description. It describes who we are: we are the "United" "States" of "America": a country comprised of states, all located in America, that have voluntarily united. Because it's a descriptive phrase, not a name, grammatically it needs an article. This is also why we say the United Kingdom: again, the name describes the country (in full, it is the "United Kingdom of Great Britain and Northern Ireland").
India, however, is a name; the word doesn't describe the country, but simply names it, and thus grammatically does not need, or merit, an article.