where did it's name originate from?
It is derived from the Classical Latin "India".
India
According to the "Oxford English Dictionary" (third edition 2009), the name "India" is derived from the Classical Latin "India", 
which continent does india belong to? The Indian subcontinent.
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India [SEP] Etymology
According to the "Oxford English Dictionary" (third edition 2009), the name "India" is derived from the Classical Latin "India", a reference to South Asia and an uncertain region to its east; and in turn derived successively from: Hellenistic Greek "India" (" Ἰνδία"); ancient Greek "Indos" (" Ἰνδός"); Old Persian "Hindush", an eastern province of the Achaemenid empire; and ultimately its cognate, the Sanskrit "Sindhu", or "river," specifically the Indus river and, by implication, its well-settled southern basin. The ancient Greeks referred to the Indians as "Indoi" (""), which translates as "The people of the Indus". The term "Bharat" (; ), mentioned in both Indian epic poetry and the Constitution of India, is used in its variations by many Indian languages.