This will do the trick (if the table is duplicates). If you want to delete the rows:
delete from duplicates d
where first_name is null and last_name is null
and 1 < (select count(*) from duplicates where phone_number = d.phone_number);
If you just want to get the new relation:
select * from duplicates d
where not (first_name is null and last_name is null
and 1 < (select count(*) from duplicates where phone_number = d.phone_number));
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