If the filename appears in the [name] field, and you want to remove the same number of characters from the start of every file you can use an expression.
In Standard View:
1) Select a few files (2 or 3 should be enough).
2) Right click on the name field of an one of them and select rename (f2).
3) To remove two digits, a period and an underscore (e.g. 01._ that's four characters), type:
=removeleft([name],4)
That will return the [name] field minus the 4 leftmost characters for the 2-3 files selected. If this is correct, select all the files you wish to rename and repeat.
If the filename isn't in the [name] field, and you'd like it to be, you can simply do the above but substitute [filename (name)] for [name]. That will fill the [name] field with the filneame, minus the first four characters.
You can then rename the actual files using wig's suggestion of Rename, Move and Copy.
More details on the expression:
http://wiki.jriver.com/index.php/Expression_Language#RemoveLeft.28.E2.80.A6.29:_Trims_characters_from_the_beginning_of_a_string