SSIS 2008: Illegal characters in path when trying to rename a file
\\\\servername\\csv\\BACKUP\\&quot; + (DT_WSTR,4)DATEPART(&quot;yyyy&quot;,GetDate()) + RIGHT(&quot;0&quot; + (DT_WSTR,2)DATEPART(&quot;mm&quot;,GetDate()) ,2) + RIGHT(&quot;0&quot; + (DT_WSTR,2)DATEPART(&quot;dd&quot;,GetDate()),2) + &quot;.csv

You almost had it here but you missed the leading and trailing quotes.
\\servername\csv\BACKUP\&quot; + (DT_WSTR,4)DATEPART(&quot;yyyy&quot;,GetDate()) + RIGHT(&quot;0&quot; + (DT_WSTR,2)DATEPART(&quot;mm&quot;,GetDate()) ,2) + RIGHT(&quot;0&quot; + (DT_WSTR,2)DATEPART(&quot;dd&quot;,GetDate()),2) + &quot;.csv

Now you're missing the leading and trailing quotes and you failed to escape your back slashes.
&quot;\servername\csv\BACKUP&quot; + (DT_WSTR,4)DATEPART(&quot;yyyy&quot;,GetDate()) + RIGHT(&quot;0&quot; + (DT_WSTR,2)DATEPART(&quot;mm&quot;,GetDate()) ,2) + RIGHT(&quot;0&quot; + (DT_WSTR,2)DATEPART(&quot;dd&quot;,GetDate()),2) + &quot;.csv&quot;
Now you've got the quotes but not escaping the backslashes
&quot;\\servername\csv\BACKUP\&quot; + (DT_WSTR,4)DATEPART(&quot;yyyy&quot;,GetDate()) + RIGHT(&quot;0&quot; + (DT_WSTR,2)DATEPART(&quot;mm&quot;,GetDate()) ,2) + RIGHT(&quot;0&quot; + (DT_WSTR,2)DATEPART(&quot;dd&quot;,GetDate()),2) + &quot;.csv&quot;
This works correctly for me in SSIS expression.

FYI
\\servername\csv\BACKUP\&quot;+1+&quot;.csv
again you are missing the leading and trailing quotes.  However this won't work because it sees 1 as an integer and you need to convert it.
&quot;\\\\servername\\csv\\BACKUP\\&quot;+&quot;1&quot;+&quot;.csv&quot;

The above works.
Normally when doing these sorts of expressions I do it iteratively.  Adding 1 piece to the expression at a time so if it breaks I know where it broke.  Remember you can click &quot;evaluate expression&quot; to see the result.
If the expression evaluates correctly but the package doesn't work then it would be another issue with the package.