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Generally the phenomenon is called the intrusive consonant.
Messenger shows us a case of "intrusive N" or "parasitic N." Nasal consonants are often used in this way, but not exclusively nasals.
From http://www.etymonline.com/index.php?term=messenger
With parasitic -n- inserted by c. 1300 for no apparent reason except that people liked to say it that way (compare passenger, harbinger, scavenger).
Please see the similar etymology for passage --> passenger.