I believe you problem can be solved by using conditions.
Create a default naming rule for site Boulevard and attach it to the business object using condition "is True" so it will always be applied unless there is other condition.
Create another condition named IsLondon using custom parameter Usersession with the expression being like in the picture attached with your London sitename.
Create another naming rule and attach it to your Business Object with the new condition created.
This method will check for User site attribute and will apply the condition.