If someone thinks like you, can he or she be your 'alter ego'?

The Oxford English Dictionary gives the current most common meaning of alter ego as ‘A person's secondary or alternative personality; a persona.’ However, the earliest meaning is ‘A person regarded and treated as another version of oneself; an intimate and trusted friend’. In that sense, alter ego could be someone who thought in the same way as you, but in using it like that you would have to be sure that the context and the circumstances ensured that you would not be misunderstood.

I would not use alter ego to to describe someone whose thoughts and behaviour usually match one’s own, if for no other reason that it has come to mean a superhero’s secret identity in popular or comic-book culture.

And doppelgänger is probably unavailable for that purpose, too, as that has too much of an eerie, supernatural connotation.

Less risky would be to call that person one’s second self. This has some currency and risks no confusion as the other terms do.