SQL Server 2016

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

CREATE TABLE Control
    ([PKey] int, [TimeStamp] datetime, [Name] varchar(10), [Price1] float, [Price2] float);

INSERT INTO Control ([PKey], [TimeStamp], [Name], [Price1], [Price2])
VALUES
    (1,'2018-10-01 09:00:00', 'Name1',120, 125),
    (2,'2018-10-01 09:10:00', 'Name1',110, 115),
    (3,'2018-10-01 09:20:00', 'Name1',101, 106),
    (4,'2018-10-01 09:30:00', 'Name1',105, 110),
    (5,'2018-10-01 09:40:00', 'Name1',106, 111),
    (6,'2018-10-01 09:50:00', 'Name1',108, 113),
    (7,'2018-10-01 10:00:00', 'Name1',110, 115),
    (8,'2018-10-01 10:10:00', 'Name1',104, 109),
    (9,'2018-10-01 10:20:00', 'Name1',101, 106),
    (10,'2018-10-01 10:30:00', 'Name1',99, 104),
    (11,'2018-10-01 10:40:00', 'Name1',95, 100),
    (12,'2018-10-01 10:50:00', 'Name1',101, 106),
    (13,'2018-10-01 11:00:00', 'Name1',102, 107),
    (14,'2018-10-01 11:10:00', 'Name1',101, 106),
    (15,'2018-10-01 11:20:00', 'Name1',99, 104),
    (16,'2018-10-01 11:30:00', 'Name1',105, 110),
    (17,'2018-10-01 11:40:00', 'Name1',108, 113),
    (18,'2018-10-01 11:50:00', 'Name1',108, 113),
    (19,'2018-10-01 12:00:00', 'Name1',109, 114),
    (20,'2018-10-01 12:10:00', 'Name1',108, 113),
    (21,'2018-10-01 12:20:00', 'Name1',105, 110),
    (22,'2018-10-01 12:30:00', 'Name1',101, 106),
    (23,'2018-10-01 12:40:00', 'Name1',102, 107),
    (24,'2018-10-01 09:00:00', 'Name2',103, 108),
    (25,'2018-10-01 09:10:00', 'Name2',101, 106),
    (26,'2018-10-01 09:20:00', 'Name2',104, 109),
    (27,'2018-10-01 09:30:00', 'Name2',106, 111),
    (28,'2018-10-01 09:40:00', 'Name2',108, 113),
    (29,'2018-10-01 09:50:00', 'Name2',108, 113),
    (30,'2018-10-01 10:00:00', 'Name2',105, 110),
    (31,'2018-10-01 10:10:00', 'Name2',103, 108),
    (32,'2018-10-01 10:20:00', 'Name2',101, 106),
    (33,'2018-10-01 10:30:00', 'Name2',99, 104),
    (34,'2018-10-01 10:40:00', 'Name2',101, 106),
    (35,'2018-10-01 10:50:00', 'Name2',104, 109),
    (36,'2018-10-01 11:00:00', 'Name2',101, 106),
    (37,'2018-10-01 11:10:00', 'Name2',99, 104),
    (38,'2018-10-01 11:20:00', 'Name2',106, 111),
    (39,'2018-10-01 11:30:00', 'Name2',103, 108),
    (40,'2018-10-01 11:40:00', 'Name2',105, 110),
    (41,'2018-10-01 11:50:00', 'Name2',108, 113),
    (42,'2018-10-01 12:00:00', 'Name2',105, 110),
    (43,'2018-10-01 12:10:00', 'Name2',104, 109),
    (44,'2018-10-01 12:20:00', 'Name2',108, 113),
    (45,'2018-10-01 12:30:00', 'Name2',110, 115),
    (46,'2018-10-01 12:40:00', 'Name2',105, 110)
;

46 rows affected

declare @EntryPrice1 float = 101.0; -- Entry when Price1 <= 101.0 (when not already Entered)
declare @ExitPrice2 float = 113.0; -- Exit when Price2 >= 113.0 (after Entry only)

WITH cte AS 
 (
   SELECT *
     ,CASE WHEN Price1 <= @EntryPrice1 THEN Timestamp END AS possibleEntry 
     ,CASE WHEN Price2 >= @ExitPrice2  THEN Timestamp END AS possibleExit
     ,Max(CASE WHEN Price1 <= @EntryPrice1 THEN Timestamp END) -- most recent possibleEntry
      Over (PARTITION BY Name
            ORDER BY Timestamp
            ROWS Unbounded Preceding) AS lastEntry 
     ,Max(CASE WHEN Price2 >= @ExitPrice2 THEN Timestamp END) -- most recent possibleExit
      Over (PARTITION BY Name
            ORDER BY Timestamp
            ROWS BETWEEN Unbounded Preceding AND 1 Preceding) AS lastExit
   FROM [dbo].[Control] 
 )
-- SELECT * FROM cte ORDER BY Name, PKey
,groupRows AS 
 (
   SELECT *
     -- if lastEntry <= lastExit we're after an exit and before an entry -> don't return this row
     ,CASE WHEN lastEntry <= lastExit THEN 0 ELSE 1 END AS returnFlag
     -- assign the same group number to consecutive rows in group 
     ,Sum(CASE WHEN lastEntry <= lastExit THEN 1 ELSE 0 END)
      Over (PARTITION BY Name
            ORDER BY Timestamp
            ROWS Unbounded Preceding) AS grp
   FROM cte
   WHERE (possibleEntry IS NOT NULL OR possibleExit IS NOT NULL)
     AND lastEntry IS NOT NULL
 )
-- SELECT * FROM groupRows ORDER BY  Name, PKey
,rowNum AS
 (
   SELECT *
     -- to get the values of the 1st row in a group
     ,Row_Number() Over (PARTITION BY Name, grp ORDER BY Timestamp) AS rn
     -- to get the values of the last row in a group
     ,Last_Value(Price2)
      Over (PARTITION BY Name, grp
            ORDER BY Timestamp
            ROWS BETWEEN Unbounded Preceding AND Unbounded Following) AS ExitPrice
     ,Last_Value(possibleExit)
      Over (PARTITION BY Name, grp
            ORDER BY Timestamp
            ROWS BETWEEN Unbounded Preceding AND Unbounded Following) AS ExitTimestamp
     ,Last_Value(CASE WHEN possibleExit IS NOT NULL THEN PKey END)
      Over (PARTITION BY Name, grp
            ORDER BY Timestamp
            ROWS BETWEEN Unbounded Preceding AND Unbounded Following) AS ExitPKey
   FROM groupRows
   WHERE returnFlag = 1
 )
SELECT Name
  ,Price1 AS EntryPrice
  ,ExitPrice
  ,Timestamp AS EntryTimestamp
  ,ExitTimestamp
  ,PKey AS EntryPKey
  ,ExitPKey
FROM rowNum
WHERE rn = 1 -- return 1st row
ORDER BY Name, Timestamp

Name	EntryPrice	ExitPrice	EntryTimestamp	ExitTimestamp	EntryPKey	ExitPKey
Name1	101	113	2018-10-01 09:20:00.000	2018-10-01 09:50:00.000	3	6
Name1	101	113	2018-10-01 10:20:00.000	2018-10-01 11:40:00.000	9	17
Name1	101	106	2018-10-01 12:30:00.000	null	22	null
Name2	101	113	2018-10-01 09:10:00.000	2018-10-01 09:40:00.000	25	28
Name2	101	113	2018-10-01 10:20:00.000	2018-10-01 11:50:00.000	32	41

Warning: Null value is eliminated by an aggregate or other SET operation.