The file name is just that a name.There are some restrictions to that name, the three letter extension to the left of the dot which is assigned by FTM, can not be changed.
There is some limitation on the characters that can be used: /, *, +, -, etc are reserved for the operating system.
The characters to the left can be just about anything, with one limitation.That limitation is on FTM backup files, *.ftmb files, FTM will append the date,YYYY-MM-DD, to what ever you name the file. FTM also append Autobackup for it autoback up file that it creates when you exit FTM.Examples: My family_2013-09-29,My family_AutoBackup
Recognizing these requirements, the file name is open to what you wish.
Being lazy my file is named "My Family" (I have all my families in one database)You could give it your family surname, My Family and My Wifes family. etc..