I am new for sharepoint nintex workflow, I would like to know if it is possible to assign task to distribution list and if yes is it possible to get the name of the person who has accepted the flexi task, as this information i would be needing ahead in the workflow.
I have found in some article that this is not possible, we are using nintex workflow 2013 on-premise
Dear,
1- Store TaskID in collection variable
2- For each ID in the collection variable, use the Query list action to query the Tasks list for "Outcome" and "Assigned To" fields.
3- Once you find the needed outcome value, use the "Assigned To" field for the same item.
Cheers 
actually the answer depends on how you configured the flexi task.
since you assign the to to a group, in order you could identify respondents you need to switch on "Create individual tasks for all group members"
further, important role play how did you configure 'Behaviour' option since different settings affects when task is considered responded and when really approved. I would recommend to study following great blogpost Do you really know the Flexi task?
based on those and whether you need single or more approvers, you might be able to get approver directly from workflow common reference variable 'Last Approver", or you might need apply a procedure as sugests, or you might even not be able to identify/have approver.
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