First of all, we need to see what kind of trademark is registered when you say "a certain name is a registered trademark (with the word R)". As long as it is not registered in category 35, because 35 protects shops and store names, self-employed individuals can still use that name as the store name.

Supplementary information answer: If "a name is a registered trademark (with the word R)" is a well-known trademark, then self-employed individuals cannot use that name as the store name.