Personally, I would go for naming them after the twelve largest moons in the solar system, since they were originally (and still are in many cultures) based on the lunar cycles, giving the months Ganymede, Titan, Callisto, etc.
What would you rename the months?
The idea that July and August were added and shifted the months to be wrong is actually a misconception afaik. The months they replaced were already basically “fiveuary” and “sixuary”.
The numbering got shifted off when they decided January should be the first month; it used to be March. February was the last month, which explains why leap days are added to February.