SQL Server 2019

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CREATE TABLE #tb_example (
    car_id INT,
    owner_id NVARCHAR(5),
    service_date SMALLDATETIME
);

INSERT INTO #tb_example (car_id, owner_id, service_date) VALUES (1, 'user2', '2016-01-02');
INSERT INTO #tb_example (car_id, owner_id, service_date) VALUES (1, 'user2', '2016-03-02');
INSERT INTO #tb_example (car_id, owner_id, service_date) VALUES (1, 'user3', '2016-11-02');
INSERT INTO #tb_example (car_id, owner_id, service_date) VALUES (1, 'user4', '2017-01-02');
INSERT INTO #tb_example (car_id, owner_id, service_date) VALUES (1, 'user4', '2017-02-12');
INSERT INTO #tb_example (car_id, owner_id, service_date) VALUES (1, 'user1', '2017-03-22');
INSERT INTO #tb_example (car_id, owner_id, service_date) VALUES (1, 'user2', '2017-03-24');

;WITH CTE AS
(
    SELECT *,           
            CASE 
              WHEN owner_id <> COALESCE(LAG(owner_id) OVER 
                                  (PARTITION BY car_id ORDER BY service_date), owner_id) 
                     THEN 1
              ELSE 0 
            END AS grp
    FROM #tb_example
)
SELECT *,
       SUM(grp) OVER (PARTITION BY car_id ORDER BY service_date) + 1 AS rnk
FROM cte 
ORDER BY service_date;

car_id	owner_id	service_date	grp	rnk
1	user2	2016-01-02 00:00	0	1
1	user2	2016-03-02 00:00	0	1
1	user3	2016-11-02 00:00	1	2
1	user4	2017-01-02 00:00	1	3
1	user4	2017-02-12 00:00	0	3
1	user1	2017-03-22 00:00	1	4
1	user2	2017-03-24 00:00	1	5