Oracle 23c

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with
 t(name,id1,id2) as (
    select 'A', to_date('01.01.2020','dd.mm.yyyy'),to_date('01.02.2023','dd.mm.yyyy') from dual union all
    select 'A', to_date('12.12.2021','dd.mm.yyyy'),to_date('20.05.2022','dd.mm.yyyy') from dual union all
    select 'A', to_date('12.12.2022','dd.mm.yyyy'),to_date('30.01.2023','dd.mm.yyyy') from dual union all
    select 'A', to_date('01.03.2023','dd.mm.yyyy'),to_date('01.04.2023','dd.mm.yyyy') from dual union all
    select 'A', to_date('01.01.2020','dd.mm.yyyy'),to_date('01.01.2024','dd.mm.yyyy') from dual union all
    select 'В', to_date('01.02.2020','dd.mm.yyyy'),to_date('01.04.2023','dd.mm.yyyy') from dual union all
    select 'В', to_date('01.05.2023','dd.mm.yyyy'),to_date('01.01.2024','dd.mm.yyyy') from dual union all
    select 'А', to_date('01.02.2024','dd.mm.yyyy'),to_date('01.03.2024','dd.mm.yyyy') from dual union all
    select 'А', to_date('01.04.2024','dd.mm.yyyy'),to_date('01.05.2024','dd.mm.yyyy') from dual
)
select *
from t
match_recognize (
   partition by name
   order by id1
   measures
      min(id1) as start_
     ,max(id2) as end_
     ,match_number() as mn
   pattern ( (a b+ c*)| (a))
   define
      b as id1 <= max(a.id2) and id2 > min(a.id1)
     ,c as id1 <= max(b.id2) and id2 > min(b.id1)
)
/

NAME	START_	END_	MN
A	01-JAN-20	01-JAN-24	1
А	01-FEB-24	01-MAR-24	1
А	01-APR-24	01-MAY-24	2
В	01-FEB-20	01-APR-23	1
В	01-MAY-23	01-JAN-24	2