Ask HN: How to deal with unequal SE levels?

I am currently in a contract at a FAANG company where I am only considered a Software Engineer (not Senior). It makes my resume look like I took a step down but I actually make more money and am still doing things at a senior level. The contract company wants me to not put the FAANG company name as my employer so this position has made my resume look terrible with a no-name employer and a step down in my role.

Has anyone dealt with this already or have any tips for dealing with this?