There is another pseudonym Dmowski used to use: R. Skrzycki
The Liga Polska had been founded in the autumn of 1887; since 1893 it had been called Liga Narodowa. The National Democratic Party emerged from it in 1893. In this circle Dmowski found his permanent intellectual and political home and soon acquired a leading position. He became close friends above all with Johann Ludwig Popławski, ten years his senior, who together with Bohusz (Joseph Potocki) published the weekly magazine "Głos" in Warsaw (since 1886). Here, but also in other journals, Dmowski's first literary works appeared in 1890, among them a novella. He was already using the pseudonym "R. Skrzycki", under which his sensational contributions "Thoughts of a Modern Poland" were to appear first.
In 1902, Dmowski again took over the management of the "Allpolnische Rundschau" and moved it to Krakow. As in 1895, this year's edition reflects Dmowski's particularly intensive collaboration. In it he also published, under his old pseudonym "R. Skrzycki", the "Thoughts of a Modern Pole", which then appeared in the following year (1903), supplemented and completed, as a book. They made a deep impression on the political consciousness of the Poles, both in contradiction and approval. These works actually established Dmowski's reputation as a political thinker.
— Erich Maschke: "Roman Dmowski", Osteuropa, Vol. 10, No. 7 (April 1935), pp. 391–410. jstor, [translated, LLC]
This bibliography confirms many instances of usage of Skrzycki as a pen name:
Bibliografia - Romana Dmowskiego (#PomnikDmowskiego. Wesprzyj budowę pomnika Romana Dmowskiego" [#Monument of Dmowskiego. Support the construction of the Roman Dmowski monument"])
Apparently, the Polish Wikipedia omits this info from his personal page, but reveals this pseudonym for the page on his Thoughts of a Modern Pole.
Whether he used any other name for his travels to Tokyo is unknown to me, as nothing of these naming circumstances appears anywhere in the literature I consulted on this. But in Tokyo, in fact once he left the borders of Russia behind, my guesses tend to assume that his real name would be used in Japan?
The Polish Wikipedia/Wikisource site only knows about these two aliases:
Author: Roman Dmowski
(Kazimierz Wybranowski, R. Skrzycki)