I tested saving and loading various slots in the versions of Chrome, Edge, and Firefox I have on my system. When opening Saves, and clicking to save in a slot, it should be prompting (thus the 'prompt()' you to ask what you want to name the slot. By default, it'll use the character name (or 'unknown') until you've gotten to the point of choosing one.
What browser and version do you have? I can try and see if I can find the problem. It could be a specific problem with the browser. And if it's more common than anticipated I can try to workaround it.