Simplest is to add a column to your table. You don't need an actual column in the DB, just an extra column in your select or a new item added to your table in code, such as this (VB):
Dim dt As New DataTable
dt.Columns.Add("ID")
dt.Columns.Add("Name")
dt.Columns.Add("DueMonth")
dt.Columns.Add("SortMonth")
Const DayMonth As String = "01 2000"
dt.Rows.Add(New Object() {101, "AAAAA", "January", Date.Parse("January" & DayMonth).Month})
dt.Rows.Add(New Object() {102, "cccc", "May", Date.Parse("May" & DayMonth).Month})
dt.Rows.Add(New Object() {103, "AAAAA", "January", Date.Parse("January" & DayMonth).Month})
Dim dv As New DataView(dt)
dv.Sort = "SortMonth"
MessageBox.Show(dv(2)(2))
How you'd do it in your SELECT statement depends on your DB type. In Oracle, it'd be something like
select to_char(to_date('January','month'),'mm')
In SQLServer, it's something closer to the code:
select DATEPART(MM, YourMonth + ' 01 2000')