OpenText EIM Redirect Issue

There is not enough information here for me to help you.

You can do this with LTM as well but as you can see when you have multiple outgoing to requests to different destinations you need to create virtual's for them as well. The problem here is I do not have a clear picture of what is happening. Can you draw up a diagram to explain the application flows that are going on here and attach to this post.

As for correct naming, the BIGIP can rename anything in the traffic flow to make it look right to the application, that is one of its strengths. The challenge for the solution designer is to clearly understand what the server is expecting.