Fact type names are generated based on the default reading for the fact type. The reading editor tool window lets you prioritize reading orders and readings, which can change the default reading. If you see an editable fact type name it is because the fact type is explicitly or implicitly objectified. Fact types are implicitly objectified if they are binary with a spanning uniqueness constraint, or n-ary (ternary, quaternary, etc.). In these cases you are actually editing the name for the associated objectifying entity type, not the fact type itself (which doesn't have a writable name field). The editable name in the properties window is a sleight-of-hand redirection.
The fact types that you can rename (namely the explicitly or implicitly objectified ones) will generally map to join tables in the relational world, which means that the names will actually be used. There is no common use for fact type names that do not map to join tables.
In the extremely early days of NORMA we did have an asserted FactTypeName field, but found that having dozens of fact types called 'FactTypeN' was much less useful than showing a generated name. When we added implicit objectification--something that we had to do during the generation stage anyway--we eliminated the fact type names. The default names for the objectifying entity types track the default fact type names, and can be restored to their default names by setting the name to an empty string.
Of course I'm curious as to the use case where this matters to you. If there is some extra data you need to collect you can always look at using the Custom Properties extension to add properties to your fact types.