Most of the Estonians with Russian names do identify as Russian, even if they aren't necessarily Russian nationals. It's an ethnic group, these are ethnic Russians.
> The reason it looks different, is because they're Estonian, so the name will be different
This is false. It's spelled the way it is spelled because that's how Estonian government wants names spelled. Also, because it would be awkward to interact with a society where most people do not know the Cyrillic alphabet.