SQL Server 2019

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select v.*
into t
from (values ('Mike', convert(date, '1/1/2019'), convert(date, ' 4/30/2019')),  
             ('Mike', convert(date, '5/1/2019'), convert(date, ' 7/31/2019')),  
             ('Mike', convert(date,'11/1/2019'), convert(date, '12/31/2019')),  
             ('Jen ', convert(date, '3/1/2019'), convert(date, ' 5/31/2019')),  
             ('Jen ', convert(date, '6/1/2019'), convert(date, ' 7/31/2019'))  
     ) v(name, startdate, enddate)
5 rows affected

select t.*
from t


name
startdate
enddate


Mike
2019-01-01
2019-04-30

Mike
2019-05-01
2019-07-31

Mike
2019-11-01
2019-12-31

Jen
2019-03-01
2019-05-31

Jen
2019-06-01
2019-07-31


select name, grp, min(startdate), max(enddate)
from (select t.*,
             sum(case when prev_enddate >= dateadd(day, -1, startdate) then 0 else 1 end) over
                 (partition by name order by startdate) as grp
      from (select t.*,
                   max(enddate) over (partition by name
                                      order by startdate
                                      rows between unbounded preceding and 1 preceding
                                     ) as prev_enddate
            from t
           ) t
     ) t
group by name, grp;


name
grp
(No column name)
(No column name)


Jen
1
2019-03-01
2019-07-31

Mike
1
2019-01-01
2019-07-31

Mike
2
2019-11-01
2019-12-31

name	startdate	enddate
Mike	2019-01-01	2019-04-30
Mike	2019-05-01	2019-07-31
Mike	2019-11-01	2019-12-31
Jen	2019-03-01	2019-05-31
Jen	2019-06-01	2019-07-31