You could use a recursive cte to get the expected result. The recursive cte uses row numbers of names sorted alphabeticaly. This is Inner Joined in unioned (recursive) part of the cte ON(n2.rn > n.rn) which ensures that you get all the combinations of current name with every name that is alphabeticaly after the current name…

WITH   --  R e c u r s i v e    C T E : 
  Recursive names ( pass, rn, name_1, name_2 ) AS
    ( Select 1, n.rn, n.name, n.name  
      From   ( Select Row_Number() Over(Order By name) as rn, name
               From tbl 
             ) n 
      Union All 
      Select pass + 1, n.rn, n.name_1, n2.name
      From   names n
      Inner Join ( Select Row_Number() Over(Order By name) as rn, name
                   From tbl 
                 ) n2 ON(n2.rn > n.rn)
      Where  n.pass < ( Select Count(*) From tbl )
   )

… resultset gives you all combinations sorted and without oposite values (e.g. ALICE-BOB vs BOB-ALICE) …

/*  Recursion ResultSet: 
pass    rn  name_1  name_2
----  ----  ------  ------
   1     1  ALICE   ALICE
   1     2  BOB     BOB
   1     3  CHUCK   CHUCK
   2     1  ALICE   BOB
   2     2  BOB     CHUCK
   2     1  ALICE   CHUCK
   3     1  ALICE   BOB
   3     1  ALICE   BOB
   3     1  ALICE   CHUCK
   3     2  BOB     CHUCK
   3     1  ALICE   CHUCK      */

… now just select distinct rows with different name_1 and name_2 …

--    M a i n    S Q L : 
Select Distinct name_1, name_2 
From names
Where name_1 != name_2
Order By name_1

/*
name_1  name_2
------  ------
ALICE   BOB
ALICE   CHUCK
BOB     CHUCK      */

See the fiddle here.

… If you add another row in your table ( ‘MIKE’ ) the result of the code above should be …

/*
name_1  name_2
------  ------
ALICE   BOB
ALICE   CHUCK
ALICE   MIKE
BOB     CHUCK
BOB     MIKE
CHUCK   MIKE      */