Could you please provide a picture of what you are referring to? I have an image of it, but it is hardly unique to the Warsaw Pact - see this US Marine c. 1918 or these American cops in the 1950s. So is that essentially what you mean, or is it something different that you are seeing with the Warsaw Pact officers?

As Georgy said, it's hardly limited to the WP, but rather the original stance taught across the world until the two-handed stances appeared. As such, it wasn't given a particular name – it was simply the correct stance. Since then, and the introduction of alternatives, it's generally referred to as the "target shooting stance" or "Olympic shooting stance", as it's the stance used in most international competition target shooting, including the Olympics.

Of course, it's not the most practical stance in combat, and as a result some effort was made to teach "point shooting" (also called combat shooting, instinctive shooting, practical shooting, especially in older text). This means the shooter simply points the pistol at the target and shoots without using the sights, as you'd use the old blackpowder pistols before sights were introduced.

Point shooting was re-popularized during WW2. Among early proponents for teaching this to soldiers were Fairbairn and Sykes, two Commando instructors who are best known for inventing the fighting knife bearing their name. While some have attributed the comeback of point shooting almost entirely to them, I'm not convinced – it's usually not as simple as that. Here is a US 1944 film which describes the difference: https://archive.org/details/Combatfiringwithhandguns

It wasn't until the late 1950's that people like Cooper and Weaver (successfully) started trying two-handed stances in practical competition shooting matches, and it took quite some time for the stance to be picked up and taught to soldiers and police even in the US. I'm hoping someone else can fill in the blanks on post-war two-handed stance development, as it's outside my area.

EDIT: I just realized I forgot about the use of the weak hand for as a support, which is a lot older than any of the stable two-handed stances. While some manuals omit it altogether, instructors clearly taught it before it was put to print. Sadly, I haven't been able to find out how widespread it was and at what times – to the best of my knowledge, it seems to have been intended for longer range shooting and teaching it largely depended on the instructor.

The most common of these "1,5 hand" stances is grabbing the strong hand from below (as in the video above), while others are simply steadying the strong hand by putting the weak hand as a fist under it, or supporting the strong arm by putting the weak hand/forearm under the strong forearm. There may well have been examples of "Weaver-ish" two hand stances before Cooper/Weaver, but I've yet to see anything but anecdotal evidence for it.

One possible reason is the sort of pistols they used. One of the most popular pistols among Warsaw Pact states was the Makarov (PM) and its various local derivatives and variants. It weighs around 0.81 kg loaded, which is lighter than almost any contemporary NATO equivalent, and is still lighter than many of the modern pistols.

It's low weight, as well as the size and the shape of the handle arguably made one-handed shooting more practical. The guides used in the Russian military haven't been changed in this respect since the Soviet times, and still recommend you use a one-handed grip when using the Makarov.