No idea at all how you are doing this. As a guess, If you use an XMLA script, you can make that dynamic and append a date stamp.You can find an example of using dynamic XMLA in this article:
Dynamic XMLA using T-SQL for SQL Server Analysis Services
In terms of overwriting, The default for the xmla script would be using <AllowOverwrite>true</AllowOverwrite>. You can change that to false but then you'd get an error if the file already exists, instead of the file being overwritten. I don't think that has anything to do with your issue, it's just an explanation of the overwrite.
The scripts won't automatically just maintain 7 copies, you'd need to delete the older copies yourself.