I'm an IT Consultant with about 8 yrs of experience. I work here in the US on a work permit, and my employer (H1 holder) is a little know firm in New York. But my complete interaction is with my client (McKinsey & Co.) and I work at the client location itself, interacting directly with the business there (5 years now...).
So my question is if I can put McKinsey in my company name on the data form (since my experience is really there as opposed to my employer which just pays me) or should it be my employer's name ? What are others in similar positions doing ?
You said it yourself: "But my complete interaction is with my client"
You don't work for McKinsey..you do work for them
Put them in the description of job duties