One title or two? Internal level titles versus what staff use with clients

Consulting engineering firm in the UAE and India, around 1,900 people. Our framework has clean internal titles by level, such as Engineer II and Senior Engineer. Client-facing staff say these do not land in the market, where every competitor's equivalent is a 'Manager' or 'Associate Director', and that it affects who clients are willing to deal with.

The proposal on my desk is a second, external title that staff can use on email signatures and proposals, chosen by the practice head. I can see the commercial case. I can also see it undoing two years of work to make titles mean something.

Does anyone run two sets of titles successfully, and what controls keep the external one from becoming the real one?