Is "New York" a Compound Word?

Yes. "New York" is a compound proper noun formed from two free morphemes:

• New (adjective)
• York (proper noun, referencing York, England)

It functions as a single lexical unit naming a specific city (and state). Compounds can be closed (notebook), hyphenated (mother-in-law), or open (New York, ice cream). "New York" is an open compound.