You could also acomplish this within a script task. Let's assume you have the following variables:

FileDirectory, string, C:\TEMP

FileName, string, SomeFileName.csv

Imports System

Imports System.Data

Imports System.Math

Imports Microsoft.SqlServer.Dts.Runtime

Imports System.IO

Public Class ScriptMain

Public Sub Main()

Dim strDate As DateTime = DateTime.Now

Dim strNewFileName As String

strNewFileName = "SampleName" & DateTime.Now.ToString("yyyyMMdd") & ".txt"

'Another Example to use yesterday's date

'strNewFileName = "SampleName" & DateTime.Now.Subtract(New TimeSpan(1, 0, 0, 0)).ToString("yyyyMMdd") & ".txt"

'

Try

File.Move(Dts.Variables("FileDirectory").Value.ToString & "\" & Dts.Variables("FileName").Value.ToString, Dts.Variables("FileDirectory").Value.ToString & "\" & strNewFileName)

Dts.Events.FireInformation(0, "", "File Renamed Succesfully", "", 0, True)

Catch ex As Exception

Dts.Events.FireError(0, "", "Source File Does Not Exist", "", 0)

End Try

'For Debugging Purposes

'System.Windows.Forms.MessageBox.Show(Dts.Variables("FileDirectory").Value.ToString & "\" & Dts.Variables("FileName").Value.ToString)

Dts.TaskResult = Dts.Results.Success

End Sub

End Class