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The graph with two vertices and $n > 1$ edges connecting them has been called the "banana graph" in a number of papers. For one example, see "Feynman Motives of Banana Graphs" by Aluffi and Marcoli, Comm. in Number Theory and Physics (2009) 1-57. (The short title of this paper is "Banana Motives", which I find endlessly entertaining.)

Does anyone know who coined the term "banana graph"?

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Not an answer to the question : in my neck of the woods, this graph is usually called a dipole. I've never heard the term banana graph. (see also – verret Nov 7 '12 at 18:25
I think the term comes from banana diagram, which seems to be used in physics since at least the first half of the 90's. Other names for the same diagram/graph seem to be basketball or sunset diagrams. The older papers are not accessible to me, so I don't know if an originator for the term is mentioned there. – Jan Jitse Venselaar Nov 7 '12 at 20:45
actually, the sunset diagram is distinct from the banana diagram (see below) – Carlo Beenakker Nov 7 '12 at 20:57

These diagrams come by different names: "banana", "water melon", "basket ball". An early reference is M. Creutz, Rev. Mod. Phys. 50, 561–571 (1978). A more recent reference is S. Groote, J.G. Körner, A.A. Pivovarov (1998).

There is a long tradition of giving fancyful names to Feynman diagrams. This is the sunset diagram:

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