Yep, you can do this in a single update. In 11g Oracle can't reference t1.custinfo_uniqueid inside the subquery. You could join t1 there, or, as you don't appear to need t1 values for row_number(), join outside the subquery.
Note - if there's no matching t2 row, you'll set t1.name to null. I'm guessing this isn't what you want. If not, you'll need to add an existence check.
create table t1 (x primary key, y ) as
select rownum x, 'oldstuff' y from dual connect by level <= 100;
create table t2 as
with rws as (
select rownum r from dual connect by level <= 5
)
select x, r, sysdate d1, sysdate-x d2, sysdate-r d3, 'newstuff' nw from t1, rws
where x <= 50;
alter table t2 add constraint pk primary key (x, r);
update t1
set y = (
select nw from (
select t2.*,
row_number() over (partition by t2.x order by d1, d2, d3) rn
from t2
) t2
where rn = 1
and t2.x = t1.x
)
where exists (
select * from t2
where t2.x = t1.x
);
50 rows updated.