The President of the United Stated doesn’t actually have the authority to tell anyone besides the executive branch what to name geographic places. So the order only forces official US government maps created by USGS and the like to be updated. Other maps can choose to update if they want to.

Open Street Map tends to reserve the “name” tag for what things are commonly called by the local community. It appears that for the Lake Ontario and The Gulf of Mexico they’ve added an “official_name:US” tag to capture the names in the executive orders.