In 2001, in Snowbird, when Agile was defined there were also representatives from FDD(1), DSDM(2) you can see it in agile manifesto history (3).
Try to search for Project Manager in the FDD and DSDM references….
So, if I am following a good logical deduction actually “Agile Project Manager” should make sense. I think Agile Project Manager does not make sense because we are still not able to transcend certain things.
Now we’re still speaking in terms of Scrum Masters and Agile Coaches and …. unable to accept things which existed from the beginning and still exists, if I can say so.
I wonder how many of so called agile folks know/read/understood or even applied FDD, Crystal, DSDM, XP….
Side note: When I speak or hear discussions about Scrum, especially when Scrum Master(s), Scrum Coaches, PO’s, management people are present, these 3 words pop into my head: “complex adaptive problems”(4). These three words combined in this way is a condensed information of an entire discipline. Are they aware of this? If yes, should this be seen in their actions?
(1) FDD: http://www.nebulon.com/articles/fdd/latestprocesses.html
(2) DSDM: https://www.agilebusiness.org/content/roles-and-responsibilities
(3) Agile Manifesto, history: http://agilemanifesto.org/history
(4) Scrum Guide: http://www.scrumguides.org/scrum-guide.html