Not to take away from Sergei's expertise, but your issue has nothing to do with vfp; it's a standard DOS renaming convention.
>>>I am using VFP 7 SP1 and trying to rename a file with VFP's RENAME command. Unfortunately, it appears that if the source file you specify doesn't have an extension, a ".dbf" extension is assumed. The file I am trying to rename does not have an extension. Any ideas?
>>
>>Try to add '.'
>>
RENAME myfile. TO mynewfile.txt
>>
>
>Perfect. Thank you again Sergey. You are God's gift to VFP.