pen (n.3) Look up pen at Dictionary.com
slang, "prison," 1884, shortening of penitentiary; earlier use (1845) probably is a figurative extension of pen (n.2).
pen (n.1) Look up pen at Dictionary.com
"writing implement," late 13c., from Old French pene "quill pen; feather" (12c.) and directly from Latin penna "a feather, plume," in plural "a wing," in Late Latin, "a pen for writing," from Old Latin petna, pesna, from PIE *pet-na-, suffixed form of root *pet- "to rush; to fly" (see petition (n.)).

Latin penna and pinna "a feather, plume;" in plural "a wing;" also "a pinnacle; battlement" (see pin (n.)) are treated as identical in Watkins, etc., but regarded as separate (but confused) Latin words by Tucker and others, who derive pinna from PIE *spei- "sharp point" (see spike (n.1)) and see the "feather/wing" sense as secondary.

In later French, this word means only "long feather of a bird," while the equivalent of English plume is used for "writing implement," the senses of the two words thus are reversed from the situation in English. Pen-and-ink (adj.) is attested from 1670s. Pen name is recorded from mid-19c.
pen (v.2) Look up pen at Dictionary.com
"to enclose in a pen," c.1200, from Old English *pennian, from the source of pen (n.2). Related: Penned; penning.
pen (n.2) Look up pen at Dictionary.com
"enclosure for animals," Old English penn, penne, "enclosure, pen, fold," of uncertain origin, perhaps related to Old English pinn "pin, peg" (see pin (n.)) on notion of a bolted gate or else "structure made of pointed stakes."
pen (v.1) Look up pen at Dictionary.com
late 15c., from pen (n.). Related: Penned; penning.