Yes, click on the FileName while the file is not open and change the name.
This will only cause issues for your solution if:
a) There are quoted text references to the file name somewhere inside the file--those will have to be found and updated
b) you have other files that contain external data source references to it. Those will fail when you rename the file.
But in the case of b) you can use FileMaker advanced to do the rename and update those references in the other files. You can also do this manually by accessing Manage | External Data Sources and updating the references in that one location.
Phil's advice is great. But just also wanted to make sure you were not talking about a file being hosted by FileMaker Server. Then you need to stop it, download it (or get from a backup) and rename it off of FMS before uploading it back to FMS.
No this is a database I developed myself years ago and I'm using it as a short to keep from starting from scratch. But, thanks.