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Is there a generally-accepted term (which has appeared "in print", in a peer-refereed, published paper) for a finitely-presented group G which has an aspherical, closed, connected, finite-dimensional manifold M for its K(G,1)?

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    I could be wrong, but is finitely-presented not implied by the other properties? Maybe the best you'll get is "$G$ is the fundamental group of a closed aspherical $n$-fold". – 2017-01-03
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    Maybe look in Shmuel Weinberger's papers and references therein? By the way, it sounds plausible that, depending on whether you mean smooth or topological manifold, you have two distinct notions. – 2017-01-03
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    I don't think this is a situation where there is a generally accepted term. But, many people would follow what you mean if you adopted some such terminology as suggested by @DanRust, or perhaps truncated it further to something like "an aspherical manifold group", particularly if you carefully define what it means. – 2017-01-03
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    @YCor: Yes, indeed, these are distinct notions in DIFF an TOP category. – 2017-01-04

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A quick google search gave "aspherical manifold groups" used in

Koji Fujiwara and Jason Fox Manning, "CAT(0) and CAT(−1) fillings of hyperbolic manifolds", J. Differential Geom. Volume 85, Number 2 (2010), 229-270.

However, this does not appear to be a common terminology. For instance, it is not used in the Manifold Atlas", http://www.map.mpim-bonn.mpg.de/Aspherical_manifolds, where such groups are consistently referred to as "the fundamental group of an aspherical closed manifold". Same in the survey

W. Lueck, "Aspherical manifolds", Bulletin of the AMS (2012) 1–17

Same in

Sylvain Cappell, Shmuel Weinberger and Min Yan, "Closed Aspherical Manifolds with Center" Journal of Topology 6 (2013) 1009–1018.

See also references I gave here in connection to the Wall Conjecture.

Thus, my suggestion is to stick with the more common terminology "the fundamental group of a closed aspherical manifold".