the curse of G-d's name also includes the simple affirmation that He does not exist
The Rambam himself writes in his Hilchos Yesodei HaTorah (Foundations of the Torah, chapter 1):
The foundation of foundations and firmest pillar of all wisdom is, To know that there is a First Being, that He caused all beings to be, and that all beings from heaven and earth, and from between them, could not be save for the truth of His Own Being.
The 9th mitzvah is that we are commanded to sanctify G-ds name, as the Sefer HaMitzvot explains:
This mitzvah requires us to publicize the true religion to the masses. This must be done without fear of retribution, to the extent that even if a powerful tyrant tries to force us to deny G‑d (exalted be He), we may not obey him. We must rather unquestioningly submit to death, not even allowing him to think that we have denied G‑d (exalted be He) [by outwardly denying Him], even if we still maintain belief in Him in our hearts. (emphasis mine)
The Gemara (Temurah 3b) also explains:
The Gemara resumes the discussion of one who curses another: Rather, the term vehifla in Deuteronomy 28:59 comes to teach what? It comes to teach that one who curses another using the name of G-d is flogged. The Gemara asks: But why not say that that verse refers to one who pronounces the name of Heaven in vain? The Gemara answers: Even if it does, is cursing another using the name of G-d any less of a sin than pronouncing the name of Heaven in vain? If one is flogged for the latter, certainly one is flogged for the former.
Also, the Shulchan Arukh (Choshen Mishpat 27:1) states (footnote 3):
One who curses an Israelite,1 and even [if] he curses himself,2 — by the [Divine] Name or by a substitute,3Mishna ibid.: ‘(If one said to witnesses, I adjure you) by Alef-Daleth (the first two letters of Adonai, the Lord) or by Yod-He (the Tetragrammaton) or by Shaddai (the Almighty) or by Ẓebaoth ([Lord] of Hosts) or by the Merciful and Gracious One, or by Him that is long-suffering and of great kindness, or by any of the substitutes of the Name, they are liable … If a man cursed himself or his fellow by any of them, he transgresses a negative precept.’ Gemara ibid. 36a: ‘R. Jannai said: This is the view of both (i.e., R. Meir and the Sages both agree that one who curses himself or his neighbour not merely by the Name, but even by any of the substitutes, transgresses a negative precept).’ or by one of the names that the heathens call the Holy One, Blessed be He,4 — if this took place in the presence of witnesses5 and [was preceded by] warning,6 he receives lashes7 on account of [the negative precept] 'Thou shalt not curse the deaf,'8 and if [the cursed person] was a Judge, he receives additional lashes on account of [the negative precept] 'Thou shalt not curse the Judges.'9 And [if one cursed by] Arur it is considered a form of curse.10