What is the technical name for the push-on type of wheels that are found on some bicycle trailers? The trailer wheels have their own axle that stays in place via a spring-loaded ball bearing.


(They are quite different from the various axles usually found on bicycles themselves; those have some kind of bolt or clamp at both ends and go into dropouts.)
They’re described in
wikipedia

Most trailers have a separate axle for each wheel, like those used on
a bicycle. These separate axles usually mount directly on the frame
using either threaded nuts, a quick-release mechanism, or some press
fit arrangement.

and in
this question

...a single sided wheelchair hub. They are light and designed so the
wheels are easily removable, which is handy for a trailer that will be
packed away often.

but is there an accepted name or term?
As various people have noted, wheelchair hub is the correct term for these one-sided, push-button release hubs. 



It goes without saying that this type of mechanism is now being widely used in cycle trailers and recumbent trikes, but we still call them wheelchair hubs even though "real" wheelchair hubs have much shorter axles than are commonly found on trailers and recumbents (see image above).