SQL Server 2019

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CREATE TABLE #names
(
	first_name VARCHAR(255),
	last_name VARCHAR(255)
)
INSERT INTO #names
VALUES
('Moe', 'Momo'),
('Moe', 'Momo'),
('Jack', 'JAJA'),
('Jack', 'Jacky');
4 rows affected

with cte as 
( select n.*, 
         count(*) over (partition by first_name, last_name) as cnt
from #names n
) select distinct first_name, 
         case when cnt > 1 then last_name else NULL end as last_name
  from cte ;


first_name
last_name


Jack
null

Moe
Momo