It sounds like the item version history does not record the 'workflow history'.
The workflow keeps a separate history for itself, this is not recorded on the List item. For instance in a document approval workflow it would not show the 4-5 approval steps, this history would be visible in the workflow but not the item history.
This post has a similar issue to yours, there is no answer as such, but the Comments give some indications for solutions.
Back to your question, you say:
But when I check Version history of Item, I see only Created By name
(in this case A) instead of modified by.
This is because the workflow is only showing the name of the person that initiated the workflow (this could be a user or a system account name). I would expect the 'Modified By' name would be the same as the 'Created By'. The changes made by users during the workflow only show in the workflow history and not the Item version history.
I must have been wrong when I previously said "the Modified By would only show if the workflow modified the item".
One thing you could try is looking in the item menu>select 'workflows'>click on the workflow you see here - there is a kind of history stored here. Maybe this info is useful to you? It is possible to edit the workflow if you wish to show additional info - you could use the 'LOG' command, so that if person 1 approves you could 'LOG - person one approval OK' and so on for each person.
If you use an APPROVAL workflow you could also try linking the workflow to a task list - this would generate Tasks for the users you specify and would also serve by giving you an additional kind of traceability.