I’m new to this and just managed to update a node of a hairsaloon since the owner has changed.
I’m using the standard browser editor, I assume its called “iD”.
However I can’t find any way to change the old text written in something pinkish on the background (osm standard layer).
Updates to data need some time to be rendered in the default map on OSM.org. Press Shift+F5 to bypass browser cache. In case there is a question to a specific object in the database it is helpfull to post the ID of the node or way (https://www.openstreetmap.org/node/5531949383).
It is also worth noting that different zoom levels update on different schedules. At the moment I see the new name at zoom level 18, but the old name at level 19.
All higher levels are updated as soon as possible, which usually means minutes, but last month OSMF servers have some problems and it takes longer and some areas still miss some z16 tiles: