Like this?

create table #tblDoc

(

FromSender varchar(150)

)

insert #tblDoc

select 'John Doe1 <John.Doe1@abcd.com>' union all

select 'John Doe2 <John.Doe2@abcd.com>' union all

select 'John Doe3 <John.Doe3@abcd.com>' union all

select 'Some longer name <LongEmailAddressHere@LongDomainName.com>' union all

select 'Short <e@e.e>'

SELECT substring(FromSender, CHARINDEX('<', FromSender) + 1, CHARINDEX('>', FromSender) - CHARINDEX('<', FromSender) - 1)

from #tblDoc

drop table #tblDoc