Welcome to the forum, Bartler!
I don't turn pens but somehow I don't think many are stained. Seems like most use darker woods for dark pens, lighter wood for light pens, figured wood for fancy pens, etc. Maybe they are stained but not that I have heard, but then I don't look at too many pens and turnings.
Maybe cheaper pens are turned using inexpensive light wood and then stained to look richer in color, don't know. But if you seal the stain with a good finish like lacquer or one of the tougher finishes available I guess the pen would look good for quite a while. If that's the case then you can use most any stain.
David