different app name on different market/country

AFAIK, yes and depends.

Depending on how different 'same app' versions are, you may instead be expected to make one app, localized for each country, rather than multiple apps, but only App Review would know what that means. You haven't talked about your app(s), so....

Perhaps if you outlined what drives your questions someone could try to offer specific advice, otherwise.

Based on language alone, I've used localized apps in the store, where the app itself is otherwise the same regardless. With a bit more work upfront, I found it easier to maintain later.

You can localize the app's name itself. And you can also localize the customer-facing store.