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I am working on a project where I refer to the RAM model, I explain what it is, but I am not sure who defined it first.

The wikipedia article is not very explicit about it, and the first citation is from 1946.

Goldstine, Herman H., and von Neumann, John, "Planning and Coding of the Problems for an Electronic Computing Instrument", Rep. 1947, Institute for Advanced Study, Princeton. Reprinted on pp. 92–119 in Bell, C. Gordon and Newell, Allen (1971), Computer Structures: Readings and Examples, McGraw-Hill Book Company, New York. ISBN 0-07-004357-4}.

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According to the chapter notes of Chapter 1 of the book "Computational Complexity: A Conceptual Perspective" by Oded Goldreich,

The RAM model is attributed to von Neumann's report [234].

where [234] refers to

J. von Neumann. First Draft of a Report on the EDVAC, 1945. Contract No. W-670-ORD-492, Moore School of Electrical Engineering, Univ. of Pennsylvania. Reprinted (in part) in Origins of Digital Computers: Selected Papers, Springer-Verlag, pages 383--392, 1982.

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