Why are you creating a List of Reqs if you are simply wanting the current "new" req?
It also appears that you are only setting the Full Name value when the original value is blank
if rq.Field("RQ_USER_04") = "" then
Also, trying to Post at this point should fail as other potential required fields are not completed yet.
Have you tried simply using the following line within the Req_New sub?
rq.Field("RQ_USER_04") = TDConnection.Customization.Users.User(rq.Field("RQ_REQ_AUTHOR")).FullName