You need to be very, very careful using this phrase: The simple answer is that they can't, and you can't allow it. It's illegal, and could cost you your license and a fine.
The words to avoid are "using my license." For a company to do electrical contracting in Washington State, they must have one, and only one, person designated as the company's Electrical Administrator. That designation must be made in a formal manner, such as a declaration by the Board of Directors, and must be reported to WA Labor & Industries. That person takes on certain responsibilities, such as ensuring compliance with codes, state laws, and safety requirements. If that person is you, then you become responsible. How would you carry out your duties with regard to those responsibilities? You can't just tell the company to put your name on the form, then collect a few extra bucks from time to time, go about your work days as you have been doing for seven years, and expect to be able to say "it wasn't my fault because I wan't there at the time" when something goes wrong.
If the company wants to assign you that role, then you have to undertake that role. It's not a "in name only" thing.
By the way, I have been an 01 (General) Electrical Administrator in Washington State for over a decade. But I have never undertaken that role. I took the test and I keep the license current only because it gives me a bit of extra credibility, when I discuss my designs with electrical contractors.