As far as I know, in general it doesn't. This was the specialty of one single cartoonist - Dmitry Moor (Orlov; 1883-1946), whose cartoons for the Bezbozhnik magazine were quite (in)famous.

I found two sources to confirm this. One is a collection of Moor's work D. Moor by R. Kaufman published in 1937 in Moscow. On p. 41 it quotes a Danish journalist's review of Moor's work:

"Его специальность — интернациональный Олимп: бога-отца, например, он изображает в виде добродушно-седого старичка с очками на лбу, христа — в виде бледного переутомленного семинариста в пенсне, св. дух изображается в виде перекормленного, разжиревшего голубя, еврейский иегова — одноглазый длинноносый Шейлок, Магомет — сладострастный неженка гарема, негритянский бог — голый каннибал в манжетах перед свежезажаренным ребенком, лежащим точно английский рождественский поросенок с яблоком во рту"

"His specialty is the international Olympus: God the Father, for example, he depicts as a good-natured, grey-haired old man with glasses on his forehead, Christ - as a pale overworked seminarian in a pince-nez, the Holy Spirit is depicted as a over-fed, fattened pigeon, Jewish Jehovah - one-eyed long-nosed Shylock, Mohammed - a sensual, tender man of harem, the Negro god - naked cannibal in front of a freshly fried child, lying like an English Christmas pig with an apple in his mouth."

The famous cartoonist Boris Yefimov, who was close to Moor, wrote in his memoir Desyat' desyatiletij: o tom, chto videl, perezhil, zapomnil (2000), p. 586:

"He started and successfully carried out the publication of the satirical magazine "The Godless man at the machine tool", on the pages of which his cartoons of the celestials of the main religious confessions appeared from issue to issue. First of all, it is the Orthodox God the Father, a fat old man with a grey beard and a halo around his bald head. His beloved Son Christ, treated as a sophisticated intellectual in a pince-nez, was always with him. At the same time - nosy and black-bearded Allah in the turban and Jewish Jehovah, for some reason one-eyed (the only eye he had, like the mythical ancient Greek Polyphemus, in the middle of his forehead). The Divine Four invariably appeared in almost every issue of "The Godless", as well as on advertising posters and calendars published by the magazine."

I haven't been able to find the explanation of why Jehovah only has one eye, but it cannot be too obscure, since the cartoons were for the common public, which is why the only plasible version is that this refers to the symbol of the All-Seeing Eye. This is a symbol which was also used in the Orthodox Church to denote God the Father's omniscience and can be seen e. g. on the Kazan Cathedral in Saint Petersburg:

https://upload.wikimedia.org/wikipedia/commons/0/08/SP_KazanskyCathedral_2370.jpg

That God the Father is Jehovah, but they're different persons in Moor's drawings, will have to be taken as a brute fact...

At least part if it was anti-sematism in addition to Atheism according to an Article in a 2008 Slavic review. Here is the abstract from and article from Robert Weiburg

In this article, Robert Weinberg explores the visual representation of Judaism and observant Jews in the Soviet journal "Bezbozhnik u stanka" (The atheist at the workbench), which appeared in the 1920s. In their efforts to promote atheism and undermine organized religion, the artists responsible for the images in this journal singled out the Jewish god to be depicted with inhuman, bestial, and bizarre features such as a single eye and a nose made out of a fist. This portrayal of Judaism and religious Jews drew upon the pervasive antisemitic tropes and motifs in Russian culture and society and served to demonize Judaism and its adherents.

In this article, Robert Weinberg explores the visual representation of Judaism and observant Jews in the Soviet journal "Bezbozhnik u stanka" (The atheist at the workbench), which appeared in the 1920s. In their efforts to promote atheism and undermine organized religion, the artists responsible for the images in this journal singled out the Jewish god to be depicted with inhuman, bestial, and bizarre features such as a single eye and a nose made out of a fist. This portrayal of Judaism and religious Jews drew upon the pervasive antisemitic tropes and motifs in Russian culture and society and served to demonize Judaism and its adherents.

https://www.jstor.org/stable/27652771?seq=1#page_scan_tab_contents