This appears to do what you want:

use tempdb

go

declare @testtable table (id int, value int, name char(4))

insert into @testtable values

(1, 10, 'test'), (2, 5, 'prod'), (3, 10, 'test'), (4, 4, 'test'), (5, 4, 'test'), (6, 10, 'test')

select * from @testtable

delete from @testtable

WHERE id in (

select t2.id from @testtable t1 INNER JOIN @testtable t2 ON t1.id = t2.id - 1 INNER JOIN @testtable t3 ON t2.id = t3.id-1

WHERE t1.name = t2.name and t2.name = t3.name)

select * from @testtable