User logging in as a "Different User"

Dears,

We are facing the below strange issue in our SharePoint farm.. After a data-center migration we did set up the F5 load balancing for our SharePoint WFE servers and now when a user say "A" access any of the SharePoint site "A" gets logged on as user "B" who has permissions to the same site.. Issue disappears when the load balancing is bypassed.. Has anyone come across this issue ? If yes pls do help me with the same. Thanks!

BR, Mukesh