All streams should have descriptions - even if the description is something like "Ignore This" or "For Modelling Purposes Only".
Some stream descriptions should be shown on the flowsheet diagrams - such as the streams entering or exiting the section, and maybe a few more important streams you wish to identify to the user of the model or to anyone with a PDF copy of the Model Diagrams.
METSIM has the concept of grouping streams by "Output Levels". By specifying the Output Level, as a parameter in each stream (or only for the streams you want to) you can control the display in many ways, but to display selected descriptions on the diagram I use the Stream Label.
The Stream Label field is directly beneath the Stream Description field on the left hand side (not the full window width "Description" field along the top) on the Stream Editor window. If I want a stream description to be displayed, I copy the stream description to the Stream Lable filed as well.
Then, I create a Display Function with the expression " Format S, VLAB S " where "format" is the APL character that looks like an O with a T overstriking it, and is the key combination Alt + "
Using this Display Expression, the stream number S and the contents of the Stream Label field are displayed, so by leaving the Label field either blank, or with a description, you can selectively display stream descriptions.