Is there an appropriate word that I can use here like "eponymous"?

Solution 1:

It's valid to use the term eponymous, but it just sounds needlessly wordy - like you'd written the above sentence and then tried too hard to get rid of the repetition.

An approach that often works well is to give the author's full name. I'll use a different example from a different field, because I don't know the authors you are talking of:

The Dunning-Kruger effect was first tested in a series of experiments published in 1999 by David Dunning and Justin Kruger.

The repetition is still there, but it's softened, and the reader feels like they're being filled in on the reason for the name, rather than just having the same words repeated at them.

Solution 2:

If you do insist on using "eponymous", it should be thus:

Johnson, Andersson and Paulsen first described their eponymous theorem in an 1865 paper.

Solution 3:

Perhaps

The eponymously named Johnson-Andersson-Paulsen theorem was first described in an 1865 paper.