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No,
Strategy is most certainly not identity.
Strategy is how to intend to achieve your goal(s). What those goals are will be influenced by your identity, and indeed, your strategy will be influenced by your identity too.
If the company is itself a brand, then the brand values will be aligned with the company's identity.
Or, to put it another way, once you've decided how you want to look in the future, strategy is how you get to that look.