Is it possible to get the user who ran a playbook from within that playbook?

checking

If you mean the user that attached a playbook to an alert that would be only in the audit log.
However it is possible to get the user that ran a manual action in a playbook (pressed the execute button) inside the python code by calling:

siemplify.original_requesting_user

@Dmitry_Sarakeev Is it possible to get the user that submitted an answer to a multiple choice question block? I'd like to be able to have the analyst's name in a follow on action. Something like, "Case was closed by [Analyst] as a false positive."

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getting back on this, currently it is not supported