Is the name Snickers a proper noun?

Yes, the Word 'snickers' (lower case s) is a common noun; the plural form of the singular noun 'snicker', a Word for a barely suppressed laugh; a Word for a thing.

The Word 'snickers' (lower case s) is also a verb, the third person, singular, present of the verb 'to snicker'; to give a small or sly laugh.

The Word 'Snickers' (capital S) is a proper noun, the name of a specific candy bar, a registered trademark of Mars, Inc.