Create Surrogate Primary Key

Let's say I have table as follows:

FirstName   MiddleName  LastName    EmailAddress
John        Middle      Steward     some@thing.com
Alice       Wonder      Land        some@thing.com
Steve       Mac         Qwak        some@thing.com
Miss        Mon         Cherie      some@thing.com
Liz         Sea         Shell       some@thing.com

This is data source with employees. As you can see, there is no primary key. Is there any way how to enhance these data with some kind of surrogate primary key? Note this is data source. I assume it is not possible to create any primary key out of the data as any time one of the row / column change, this will also lead to change of the surrogate primary key. Correct? Or is there any way?

These data are meant to be loaded into DWH using SSIS. As there should be some Lookup transformation, I need to have primary key in the source data set.