Why is a push-pull converter named push-pull?

Form the same wikipedia article

The term push–pull is sometimes used to generally refer to any converter with bidirectional excitation of the transformer.

We need to let the word 'generally' be as general as we like.

To pick apart your specific query -

The operation of the circuit means that both transistors are actually pushing, and the pulling is done by a low pass filter in general, and by a center tap of the transformer in the converter application. But because the transistors push in an alternating fashion, the device is called a push-pull converter.

I would think of both transistors of a centre-tapped transformer converter pulling, with the centre-tap being the thing they're pulling against. But that's just me.

The reference to a low pass filter is a mystery to me. That is the only reference to a low pass filter in the article. A low pass filter is not needed to make a push-pull transformer converter work. I think an editor must have been over zealous with cut'n'pasting something not understood. I might just go in there and remove it myself. (done, let's see if anybody objects).

Perhaps it's more understandable in historical context.

The term dates back the better part of a century, when only "N-type" (if you will) devices existed -- vacuum tubes. Since complementary devices didn't exist, there was no complementary totem-pole configuration that could be most symmetrically called "push-pull"; rather, this term was used for the center-tapped transformer coupled version. The term instead contrasts with the "single ended" configuration, which used a single winding on a transformer.

Note that a transformer was (almost*) always required because vacuum tubes have such high output impedances (~kΩ), compared to typical loads (speakers 4-16Ω, radio transmitters 50/75/300Ω, audio line / telephone 600Ω, etc.).

*There were some dabblings with OTL (output transformer-less) configurations, from time to time, but nothing really caught on, at least that's my understanding. Not having complementary devices, a totem-pole circuit always had to make some kind of compromise, as far as how to get enough gain to drive the high-side device (which is a cathode follower) and how to balance current flow (and distortion) in the low-side (which is common-cathode). The most prominent was probably by Philips: see The SPP Amplifier | audioXpress. As you can see, it's mainly made possible by the unusual extremely high voice-coil impedance.

Also it probably goes back even further as a mechanical term, but I'm afraid I don't know nearly enough mechanical engineering history to explore that. Offhand, for example: Push-Pull Linkage - Design and Technology Online The most direct analogy would be two tension links (ropes/belts/etc.) on a bell crank, which both strictly pull, but one can be said to push by the linkage.