Client wants contract in my name instead of LLC

I have a single member LLC, which is a pass through entity. all the taxes pass through to me at the end of the year. I have a client who wants me to redo a contract using my name instead of my LLC. Their policy is that the contract must match exactly the name on the W9. I believe I really should be doing the contract in the name of my LLC correct? Since I'm a single member LLC, the correct way to fill out the W9 is to put my name on the first line, and then my LLC on the second line. Is th...