MySQL 8.0

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CREATE TABLE address
    (`ID` int, `Name` varchar(4), `Address` varchar(15))
;
    
INSERT INTO address
    (`ID`, `Name`, `Address`)
VALUES
    (1, 'Tom', '123 Fake St.'),
    (2, 'Paul', '81 Second Ave.'),
    (3, 'Mark', '1001 Market St.'),
    (4, 'Tom', '123 Fake St.'),
    (5, 'Tom', '903 Castle St.'),
    (6, 'Pete', '14 Circle Dr.')
;

Records: 6  Duplicates: 0  Warnings: 0


SELECT
DISTINCT `Name`
FROM address a1
WHERE (SELECT COUNT(*) FROM address a2 WHERE a1.name = a2.name) > 1
  AND (SELECT COUNT(DISTINCT `Address`) FROM address a2 WHERE a1.name = a2.name) > 1


Name


Tom


WITH CTE as
(SELECT name,
  COUNT(*) count_,
  COUNT(DISTINCT `Address`) count_a
FROM address
GROUP By name)
SELECT
DISTINCT `Name`
FROM CTE WHERE count_ > 1 AND count_a > 1


Name


Tom