You can just create a copy of the database file with the new database name, that is assuming you want all the data as well. This can be done without connecting to/opening the database by standard File handling.
- The database name is only significant as the file name.
Another way is to use VACUUM INTO 'file';
again this copies all data, this does require the database to have been connected as the above is an SQL statement.
- e.g.
VACUUM INTO 'E:\Navicat\SQlite Databases\myOtherDBName';
(Windows)
- see VACUUM
If you don't want the data then when connected to the new database you can delete the rows in all the tables followed by a VACUUM (if you wish). This would probably be best done within a transaction.