Eddie being Monroe's first name is not canon and has been something incorrectly spread or mentioned as fact by some of the Grimm fan base -- the story behind this is that it was in one of the early drafts of the Pilot episode, but eventually, this was scrapped.  Silas Weir Mitchell has confirmed that Monroe is known only as just that on the show, "Monroe," and there were several clues throughout the show that alluded to his last name not being known; in a few cases, the writers kinda just jokingly teased the fans about it too.  I kinda wish more Grimm fans paid attention to the Wiki on this particular topic so that the whole Eddie thing wouldn't be spread as fact, but if you need a few sources on Monroe being only known as Monroe, I can point you to a few examples or a site or two I used to reference on this.

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