Can a temporary table be shared across sessions?
Local table tables should never be shared across sessions. As you've pointed out, they are only visible to the session that created them and are destroyed when the creating session is terminated, or you drop them.

Global temporary variables are visible to all sessions, but you'd need to define them with the double hash i.e. ##temp, for them to be defined as global.

As for putting a suffix on the table name when creating it, you're wasting your time, as SQL Server does that anyway.

CREATE TABLE #temp (Name VARCHAR(20));

USE tempdb;
GO

SELECT name FROM sys.tables WHERE name LIKE '#temp%';


For me, this returns

#temp_______________________________________________________________________________________________________________00000000004C


However, as Aaron Bertrand pointed out in this answer:


  if you call everything #temp, or #t, or #x, then it's possible that such a table already exists from an outer scope prior to calling the procedure.


In this case, you could be sharing the temp table between a top-level process and a number of different procedures that it calls within that process. This of course could lead to data corruption, depending on how you defined and constructed your temporary table.