Correct me if I am wrong here
But this should be done according to how the client wants - with all lowercase. As that is how they are branding themselves and will be on all official documents, press releases, basically anything.
I heard that google places and other similar services will pick up citations and for citations to best impact things they need to be consistent all across the board. I worked for check n go at one point and t hey had a problem where it was coming in as Check in Go, Check n Go, Check 'n Go, etc etc and it was impacting them in ways.
So I would just do which ever way the client wants and keep it consistent.