If you are referring to the file names of the saved scanned images, the name is provided by the client application or in case the client does not care about the name , the scanner twain driver is using a default name. Normally there is no way for the end user to change the name before the images are acquired.
If you are referring to the temporary names of the scanned images as they appear in the client application window, these are the default names the application is using internally and again are normally not modifiable.
There is an extremely remote possibility that a scanner driver or a client application is retrieving the base name from a database of configuration settings residing in the registry or somewhere else on your hard drive, though I wouldn’t count on this.
If you are interested in modifying not a full name but only the number assigned to the acquired image/file (and if this number is not reset to 0 or 1 every time you connect to the scanner), this I believe is possible since the latest used number must be stored somewhere and chances are it is stored in the registry. The location would depend upon the scanner.
In fact there exist too many different scenarios and there is no guarantee that any of those applies to your situation.
Hope this helps.