The name of a 4D database opened with a 4D application is determined by the name of its structure file. For a project mode database, this is the .4DProject file; for a binary mode database, it's the .4DB file.
In most cases, as long as there are no self implemented items, such as code or dependencies tied to the original name, the structure file can be safely renamed. The next time the database is opened, it will adopt the new name.

It should also be notted that settings like the Publication name default to using the database name. If the database is renamed, this setting will also change unless a specific publication name has been manually set.