1/ SYS_GUID does not return a VARCHAR2 but a RAW of 16 bytes.
2/ Nothing prevents you from creating your own function, for instance using one of the timestamp functions.

Declare
x varchar2(40);
val varchar2(40);
Begin
Select sys_guid() into x from dual;
pkg.set_parameter(x,'Testvalue');
select sys_context('parameter',x) into val from dual;
dbms_output.put_line(x);
end;

PROCEDURE Set_Parameter
(
p_name   IN  VARCHAR2,
p_value  IN  VARCHAR2
) IS
BEGIN
  DBMS_SESSION.set_context('parameter', p_name, p_value);
END set_parameter;

ORA-28106: input value for argument #2 is not valid
ORA-06512: at "SYS.DBMS_SESSION", line 122
ORA-06512: at "PKG", line 77
ORA-06512: at line 7
28106. 00000 -  "input value for argument #%s is not valid"
*Cause:    Input values for the argument is missing or invalid.
*Action:   Correct the input values.

I think you have misunderstood the arguments for dbms_session.set_context. The second argument is indeed limited to 30 bytes, but that is the name of the attribute, not the value. You'ld put the sys_guid() into the third argument, which can be 4KB.

 procedure set_context(namespace varchar2, [b]attribute varchar2[/b], value varchar2,
                        username varchar2 default null,
                        client_id varchar2 default null);
  --  Input arguments:
  --    namespace
  --      Name of the namespace to use for the application context
  --    attribute
  --      Name of the attribute to be set
  --    value
  --      Value to be set
  --    username
  --      username attribute for application context . default value is null.
  --    client_id
  --      client identifier that identifies a user session for which we need
  --      to set this context.
  --
  --

For example there is a procedure, can not we execute the procedure multiple time in one session simultaneously?!!!

For example in a .net application there is a session to database, two thread ( or more) call a function from data access layer, that this function calls the procedure from database, two thread can call this function simultaneously so procedure is called two times at same time.

In that case, each thread will use a different database session.

But each will be separate & distinct Oracle session.
Please stop dreaming about some mythical fantasy & just join us in the real World.

One static connection to database is open and all threads use it.

Yes, but not at the same time. Talk to your apps server administrator, ask him to explain how it manages connection pooling.

For example, an ID like "username-yyyyddmmhhmiss" might be "good enough" for a lot of use cases

This is a good idea, thanks.

2/ Nothing prevents you from creating your own function, for instance using one of the timestamp functions.

Kind of what I said in my first answer: