I don’t think it should matter which name gets listed first. If you are going to have multiple names in the name tag, it should be because they are equally important. If one name is important enough to be listed first, it should instead be the only name in the name tag, and the others can be in alt_name or name:language. You likely would not even be able to enforce any sort of ordering rule, and it would likely be decided by whoever happens to map the object first.
This is because of my recent experience cleaning up the cuisine tag, which make extensive use of semi colon delimited lists. For years the wiki told mappers to “Order them based on the order listed on signage, or subjective sense of importance, falling back to alphabetical”. Even so, mappers didn’t seem to apply any consistent ordering, and even different branches of the same chain restaurant in the same city often had different orders or different lists of values entirely. Now the wiki just says “The order is not important”.