SQL Server 2019

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4 rows affected

;WITH CTE AS (
   SELECT Name,StartTime,EndTime
   FROM T1
   UNION ALL
   SELECT Name,DATEADD(MINUTE, 1, StartTime) ,EndTime
   FROM CTE 
   WHERE DATEADD(MINUTE, 1, StartTime) <= EndTime
) 
SELECT Name,
       MAX(CASE WHEN t2StartTime IS NULL THEN 'Pre-Run' ELSE 'RUN' END),
       MIN(CASE WHEN t2StartTime IS NULL AND DATEADD(MINUTE, - 1, StartTime) > minTime 
          THEN DATEADD(MINUTE, - 1, StartTime) ELSE StartTime END) starttime,
       MAX(CASE WHEN t2StartTime IS NULL AND DATEADD(MINUTE, 1, StartTime) < maxTime 
          THEN DATEADD(MINUTE, 1, StartTime) ELSE StartTime END) endtime
FROM (
 SELECT c.*,
        ROW_NUMBER() OVER(ORDER BY c.StartTime) -
           ROW_NUMBER() OVER(ORDER BY t2.StartTime) grp,
        t2.StartTime t2StartTime,
        MIN(c.starttime) OVER(partition by c.NAME) minTime,
        Max(c.starttime) OVER(partition by c.NAME) maxTime
  FROM CTE c 
  LEFT JOIN T2 t2
  ON  c.StartTime BETWEEN t2.StartTime AND t2.EndTime
  AND c.Name = t2.Name
) tt
GROUP BY grp,Name
ORDER BY 3

Name	(No column name)	starttime	endtime
C1	Pre-Run	01:00:00.0000000	01:10:00.0000000
C1	RUN	01:10:00.0000000	01:20:00.0000000
C1	Pre-Run	01:20:00.0000000	01:30:00.0000000
C1	RUN	01:30:00.0000000	01:40:00.0000000
C1	Pre-Run	01:40:00.0000000	01:50:00.0000000
C1	RUN	01:50:00.0000000	01:55:00.0000000
C1	Pre-Run	01:55:00.0000000	02:00:00.0000000