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Doesn't look to be in the stable provider, but you could use the native provider for just the alias resource:
<https://www.pulumi.com/registry/packages/aws-native/api-docs/stepfunctions/statemachinealias/|https://www.pulumi.com/registry/packages/aws-native/api-docs/stepfunctions/statemachinealias/>

I think alias won’t give me what I looking for.. because it’s not dynamic name..
I need to have history executions with different column name which include relevant data of that execution
and not just GUID..

I'm not sure you can setup an alias for an individual execution, only an alias for the state machine itself

For drilling down on a per-event/request/execution basis, I had an alright experience with aws x-ray. Perhaps this will help?