Should my client change its name?

This is more of a technical question rather than design. I have a client with a foodtruck and their website and Google account is getting quite some traffic. (300 visitors a month, 60 phone calls from Google) He has a foodtruck on a prime location, so he doesn't rely on the website for customers really, but people use it see his menu and get directions. His current name is an abbreviation like ggc-chicken and he wants to change it to Grilled Chicken (it looks a bit dull in English but translated the new name is WAY better). How can we change the name without losing traffic? For sure I will have his old domain point to the new one. What else should I consider?