the name of the session is not the issue.
the session contents for each browsing session that is open are stored in a separate memory space, and only accessible by the browser that initiated the session.
John doe is on one computer and browses to your site starting a browsing session. the session is given the id 1234.
in your application you define a session:
Foo = Bar
this is persisted through the sessionID of 1234
Jane Doe visits your site and starts a new session which is given the ID 5678. Your application sets the session:
Foo = Foo
Jane will not be able to see the value of Foo that is set for John because she can only see the session contents for her ID 5678.