If you have not sorted this yet, I would suggest that you save the model as a Python script and add a variable line to the script (use notepad etc) under "gp.AddToolbox....." like:
VAR1 = gp.getparameterastext(0) #This is the variable for arcmap field they will type May2008 in
And then in the output path on the .img file type this in front of ".img"
+VAR1+".img" #this adds the variable to the raster output filename
Then in arcmap. Adds the py script to an arcmap toolbox. In the parameter settings add a "display name" called "name" and set the data type as "string"
Hope this helps???