SQL Server 2019

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CREATE TABLE Data
(
  name varchar(255),
  date DATETIME,
  happiness INT NULL
)
INSERT INTO Data
VALUES
  ('John', '2020-01-03', 20),
  ('John', '2020-01-04', NULL),
  ('John', '2020-01-05', NULL),
  ('John', '2020-01-06', NULL),
  ('John', '2020-01-07', 18),
  ('Mary', '2020-01-01', 35),
  ('Mary', '2020-01-02', NULL),
  ('Mary', '2020-01-03', -15),
  ('Mary', '2020-01-04', NULL),
  ('Mary', '2020-01-05', 0)
10 rows affected

;WITH DataC AS(
  SELECT ROW_NUMBER() OVER (PARTITION BY name ORDER BY date) AS ID,
    [name],
    [date],
    [happiness]
  FROM Data
), CTE AS (
  SELECT ID,
    [name],
    [date],
    [happiness]
  FROM DataC
  WHERE ID = 1
  UNION ALL
  SELECT d.ID,
    d.[name],
    d.[date],
    COALESCE(d.[happiness], c.happiness) AS happiness
  FROM DataC d
  INNER JOIN CTE c ON c.Name = d.Name AND c.ID = d.ID - 1
)

SELECT * 
FROM CTE
ORDER BY name, date


ID
name
date
happiness


1
John
2020-01-03 00:00:00.000
20

2
John
2020-01-04 00:00:00.000
20

3
John
2020-01-05 00:00:00.000
20

4
John
2020-01-06 00:00:00.000
20

5
John
2020-01-07 00:00:00.000
18

1
Mary
2020-01-01 00:00:00.000
35

2
Mary
2020-01-02 00:00:00.000
35

3
Mary
2020-01-03 00:00:00.000
-15

4
Mary
2020-01-04 00:00:00.000
-15

5
Mary
2020-01-05 00:00:00.000
0

ID	name	date	happiness
1	John	2020-01-03 00:00:00.000	20
2	John	2020-01-04 00:00:00.000	20
3	John	2020-01-05 00:00:00.000	20
4	John	2020-01-06 00:00:00.000	20
5	John	2020-01-07 00:00:00.000	18
1	Mary	2020-01-01 00:00:00.000	35
2	Mary	2020-01-02 00:00:00.000	35
3	Mary	2020-01-03 00:00:00.000	-15
4	Mary	2020-01-04 00:00:00.000	-15
5	Mary	2020-01-05 00:00:00.000	0