October is the tenth month of the year with a name that says eight. It is a leftover from a calendar that no longer exists.
The word is Latin. Etymonline traces October to Latin October (mensis), "the eighth month." It is built on octo, "eight." That root goes back to Proto-Indo-European, and it also gave English eight itself, by way of Old English eahta.
Eight was the right number in the old Roman year. Britannica reports that, by legend, Romulus set up a calendar of ten months and 304 days. The year began in March. Its months were Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November and December. Britannica notes that the last six names match the Latin numbers five through ten.
So October was eighth, September was seventh, November was ninth and December was tenth. Etymonline makes the same point about December: it comes from Latin decem, "ten."
The extra months came later. Britannica credits Numa Pompilius with adding January and February, which turned the year into twelve months. January ended up at the front, and every month from March onward slid two places down the count. The names stayed put. Britannica says the year had become hopelessly confused by the first century BCE. Julius Caesar's reform in 46 BCE created the Julian calendar, and the number-names survived that too.
Why the names survived is not explained in the sources checked here. Wikipedia says only that October kept its name when January and February were added. Etymonline quotes T. G. Tucker's view that the first five months were named for their places in the farming cycle.
October reached English in late Old English. It pushed aside the native name winterfylleð, which Wikipedia says was used because winter was supposed to begin at that month's full moon.
Russian borrowed the Latin name too. The October Revolution of 1917 fell on November 7 in the modern calendar, because Russia still used the old one and counted it as October 25.