Loading a file using sql loader having header record which needs to be column 1 in the table to distinguish client name

Question

I have 3 clients sending their own data files which have the same detail record layout which needs to insert in the same staging table and they are distinguished by header record.

File 1

Clientname1 date
Field1 Field2 Field3

....
....
....

File 2

Clientname2 date
Field1 Field2 Field3
....
....
....

I want to basically load these 3 files in same staging table but with column 1 of the table as header clientname record so I can distinguish which client file got loaded in same staging table. How do I add header record as column 1 in same staging table? When we append the files there is no way to know which client sent it as all detail records are exact same.

The output in table should look like

Clentname1. Field1. Field2. Field3
Clentname1. Field1. Field2. Field3
Clentname1. Field1. Field2. Field3
Clentname2. Field1. Field2. Field3
Clentname2. Field1. Field2. Field3
Clentname2. Field1. Field2. Field3
Clentname3. Field1. Field2. Field3
Clentname3. Field1. Field2. Field3
Clentname3. Field1. Field2. Field3

Thank you