When two black holes merge, and presumably when a hole and a condensed object or two condensed objects merge, there must be a period when two or more singularities exist within a single event horizon. That would make the horizon non spherical and presumably radiating. I presume this is the mechanism for the "ring-down" radiation from black hole mergers. Something similar must occur when two condensed but not singular objects merge, and this signal could be the "echo" claimed to be detected in this report. I don't have the math needed to predict the shape of such a signal, and must ask the relevant community for assistance.
The generic ring down mechanism is located outside the event horizon AFAIK, but seems hard to model - event horizons are global properties (but yeah, so is the coupling near field to free wave of antennas, so YMMV). To get a gravity wave source you need a quadrupole mass energy distribution, but you get that from the merging fields (or potentials, if you want to use those).
Classically an event horizon is spherical if static, but I assume you are looking for something like this [
https://phys.org/news/2019-11-numerical-evidence-merger-motss-binary.html ]:
"In their study,
published in Physical Review Letters, they collected observations that could offer exciting new insight into the merger of marginally outer trapped surfaces (MOTSs) in a binary black hole (BBH), a system consisting of two black holes in close orbit around each other.
"It is an underappreciated fact that event horizons are not really very useful for studying astrophysical properties of black hole mergers," the researchers told Phys.org via email. "What is much more useful are surfaces which go under the boring name of marginally outer trapped surfaces (marginal surfaces or MOTS in short). This uninteresting name hides their importance in understanding
black holes.""
The MOTS is roughly the same as the inner horizon of real (rotating and/or charged) black holes, I think [
https://en.wikipedia.org/wiki/Trapped_surface ,
https://en.wikipedia.org/wiki/Reissner–Nordström_metric ]. You can handle them analytically if the black hole was collapsing spherically, which AFAIK is the odd case of gravity systems despite the inner heating - Rayleigh-Taylor instabilities [
https://en.wikipedia.org/wiki/Rayleigh-Taylor_instabilities ] are overcome.
There is a video (and it tentatively justifies my MOTS = inner horizon identification).