By the way, an ejector nozzle like that on the M88 engine is still convergent-divergent. There's seems to be some confusion about this here. The central air flow from inside the smaller inner nozzle expands out through the larger diameter outer nozzle. Its just normally a little less efficient than an iris nozzle - which effectively puts a third ring of petals sealing the inner ring to the outer ring.
Not just here - even nozzle terminology in professional literature isn't exactly stringent or consistent in this regard. I've seen a SNECMA document calling the M88 nozzle convergent (though to be fair, it was written/translated in/to English and which clearly not the authors' strong suit)! The whole issue is compounded by manufacturers occasionally coining their own names and the fact that the secondary (ejector) nozzle sometimes isn't part of the engine at all, rather than airframe-mounted (SR-71, MiG-23, F-106). This outer nozzle need not be variable, BTW - see the F-106.
I prefer to call designs of the M88 (and related) kind convergent ejector nozzles for all the reasons you state, which seems to get the essential points across without too much confusion. A convergent nozzle (in the literal sense) has no supersonic expansion, hence the ejector part, but it remains suitably distinct from "convergent/divergent" which in this context implies both parts are mechanically controlled. The term iris nozzle for the latter type is pretty uncommon and has significant potential for confusion with iris-type throttle restrictors, so is a case in point really. Last but not least, what is called a bell nozzle in rocketry is technically also a (fixed, contoured) convergent/divergent nozzle...