SQL> -- connected as LOCAL
SQL> create table test (id number);

Table created.

SQL> insert into test (id) values (100);

1 row created.

SQL> commit;

Commit complete.

SQL> grant select on test to remote;

Grant succeeded.

SQL> -- now, connect as REMOTE
SQL> connect remote/pwd@ora
Connected.
SQL> -- this is what you tried, and it didn't work (obviously, as there's no TEST table in REMOTE)
SQL> select * from test;
select * from test
              *
ERROR at line 1:
ORA-00942: table or view does not exist


SQL> -- as suggested by BlackSwan, use owner's name (LOCAL)
SQL> select * from local.test;

        ID
----------
       100

SQL> -- or, create a synonym ...
SQL> create synonym test for local.test;

Synonym created.

SQL> -- ... so that you could avoid naming owner's name (remember, we're still connected as REMOTE)
SQL> select * from test;

        ID
----------
       100

SQL>

create user "REMOTE_01" identified by "PASSw";
grant create session to "REMOTE_01";
GRANT SELECT ON "LOCAL_01.table1" TO REMOTE_01;
GRANT SELECT ON "LOCAL_01.table2" TO REMOTE_01;
GRANT SELECT ON "LOCAL_01.table3" TO REMOTE_01;

conn REMOTE_01/PASSw@MYDB
select * from LOCAL_01.table1;

GRANT SELECT ON 'LOCAL-01.table1' TO "REMOTE_01"

GRANT SELECT ON "LOCAL-01.table1" TO "REMOTE_01"

GRANT SELECT ON LOCAL-01.table1 TO "REMOTE_01"

SCOTT@orcl_12.1.0.2.0> connect scott/tiger@orcl
Connected.
SCOTT@orcl_12.1.0.2.0> create user "LOCAL-01" identified by "LOCAL-01";

User created.

SCOTT@orcl_12.1.0.2.0> alter user "LOCAL-01" quota unlimited on users;

User altered.

SCOTT@orcl_12.1.0.2.0> grant create session to "LOCAL-01";

Grant succeeded.

SCOTT@orcl_12.1.0.2.0> grant create table to "LOCAL-01";

Grant succeeded.

SCOTT@orcl_12.1.0.2.0> connect "LOCAL-01"/"LOCAL-01"@orcl
Connected.
LOCAL-01@orcl_12.1.0.2.0> create table table1 as select * from dual;

Table created.

LOCAL-01@orcl_12.1.0.2.0> grant select on table1 to scott with grant option;

Grant succeeded.

LOCAL-01@orcl_12.1.0.2.0> connect scott/tiger@orcl
Connected.
SCOTT@orcl_12.1.0.2.0> create user "REMOTE_01" identified by "PASSw";

User created.

SCOTT@orcl_12.1.0.2.0> grant create session to "REMOTE_01";

Grant succeeded.

SCOTT@orcl_12.1.0.2.0> grant select on "LOCAL-01".table1 to "REMOTE_01";

Grant succeeded.

SCOTT@orcl_12.1.0.2.0> connect "REMOTE_01"/"PASSw"@orcl
Connected.
REMOTE_01@orcl_12.1.0.2.0> select * from "LOCAL-01".table1;

D
-
X

1 row selected.

SQL> --
SQL> select username
  2  from dba_users
  3  where upper(username) like 'LOCAL%'
  4  order by 1;

no rows selected

SQL> --
SQL> create user local_01 identified by fubar;

User created.

SQL> create user local-01 identified by fubar;
create user local-01 identified by fubar
                 *
ERROR at line 1:
ORA-00922: missing or invalid option


SQL> create user "local-01" identified by fubar;

User created.

SQL> select username
  2  from dba_users
  3  where upper(username) like 'LOCAL%'
  4  order by 1;

USERNAME
--------------------------------------------------------------------------------
LOCAL_01
local-01

2 rows selected.

SQL> --
SQL> drop user local_01;

User dropped.

SQL> drop user local-01;
drop user local-01
               *
ERROR at line 1:
ORA-00921: unexpected end of SQL command


SQL> drop user "local-01";

User dropped.

SQL> --
SQL> spo off