Is SERVICE_NAME forced to be unique per logical database within a network? Would it have sense the opposite? I like to know your opinion on these two sentences to see if I understood correctly the concept.

Put RAC configuration aside, I am talking about logical databases, I understand RAC is like a group of hosts serving same logical database by means of analogous instances. 

I am talking about the uniqueness of SERVICE_NAME in a network. I also understand that 2 SERVICE_NAME cant point one database, but I would like to know whether two different DATABASES with their unique DB_NAME and SID may and are likely to be useful in some way if they expose same SERVICE_NAME.
The same SERVICE_NAME can run in multiple instances with a RAC, and in a physical standby database, those services also exist.  In fact, you'd need them to be running in order for failover to work.

Service name from a uniqueness perspective only matters in terms of being unique within a particular listener's purview; it's how the listener routes connections.  What would happen if multiple unique databases served by the listener each registered the same service?  How would it choose between/among them?