Here is one option ..
SSIS - SQL Task >>
In Execute SQL Task Editor
General - SQLStatement ..
Code..
DECLARE @Fname varchar(50)
SET @Fname = ? -- filename passed to variable
INSERT INTO dbo.FilesImported
SELECT @Fname
In Execute SQL Task Editor >>
Parameter Mapping ..
Add >>
Variable Name = User::FileName
Direction = Input
Data Type = VARCHAR
Parameter Name = 0
Parameter Size = -1