So.... BOOTS the chemist. I don’t want to be frightfully pedantic however...
If it is the Chemist belonging to Henry Boot the it is Boot’s Chemist.
If it is the definite article the it is The Chemist and yer man doesn’t get his name in there.
If he wants the definite article then it would be Boot The Chemist.
I can’t find a grammatical point where Boots is the name of the shop.