How do you determine who it should be assigned to? If it's something that can be done through logic/branching in Survey Flow, you can set an embedded data field equal to the username of the person you want to assign it to. Then in the workflow, you need to set an additional field within the ticket "Q_TicketOwner" and set it to this embedded data field.
Have a default person assigned at the top on the Owner field in case there is a problem with assigning it to the embedded data field (e.g. the person no longer there, etc.)
Not sure what the email issue may be - perhaps because you are assigning to a team.

InessaG thank you for this! We actually have the information on who it should be assigned to attached to the respondent in the directory through a field called Advisor_ID.
We did try setting the data field as Q_TicketOwner = Advisor_ID, but in testing this we couldn't see an option to filter tickets through Q_TicketOwner and it still sets the owner to the whole team. I.e. the whole team is able to view the ticket and it's not directly assigned to just one person. Do you have any idea how to fix this?

I suggest you reach out to support then. In theory this should work.
Some issues could be that the Advisor_ID doesn't match exactly to user id, etc. They'll be able to advise.

@helnour did you get an answer back from support on this? We are also looking to dynamically assign