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?
edit: Simply using the numbers is already a thing (see, for example, 2026-01-01. January is represented as month 1), and reordering the existing month names would be a real headache, as it would be difficult to tell whether you are reading a date using the old or new naming scheme.
In which language, English? Though why would renaming them in English require the approval of everyone in the world?
I’d say you don’t even need the approval of everyone living in an English-speaking country. It’s not like the US and UK use all the same words, for example. I think it’s fine for one English country to unilaterally rename them, no need for wider approval.