Need help with Update Join Query

Question

Hello, I am trying to update PID of #child table with PID of #parent table if "lastname & firstname are matches in both table" but my update query is giving some error. Please help and correct the update query. I am also trying to remove any
blank space from starting and ending.
drop table #parent,#child
create table #parent (PID varchar(10), lastname varchar(50), firstname varchar(50))
insert into #parent values ('100','Josheph','Sumali')
insert into #parent values ('400','Karen','Hunsa')
insert into #parent values ('600','Mursan  ','  Terry')
create table #child (PID varchar(10), lastname varchar(50), firstname varchar(50))
insert into #child values ('2','Josheph ','Sumali   ')
insert into #child values ('5','Karen','Kunsi')
insert into #child values ('6','Mursan ','Terry ')
Update #child
set PID = p.PID
from #child C Join
#parent p ON c.LTRIM(RTRIM(lastname) = p.LTRIM(RTRIM(lastname)
AND c.LTRIM(RTRIM(firstname) = p.LTRIM(RTRIM(firstname)
/* Requested Output */
PID        lastname      firstname
100        Josheph       Sumali
600        Mursan        Terry

Answer 1

create table #parent (PID varchar(10), lastname varchar(50), firstname varchar(50))
insert into #parent values ('100','Josheph','Sumali')
insert into #parent values ('400','Karen','Hunsa')
insert into #parent values ('600','Mursan ',' Terry')
create table #child (PID varchar(10), lastname varchar(50), firstname varchar(50))
insert into #child values ('2','Josheph ','Sumali ')
insert into #child values ('5','Karen','Kunsi')
insert into #child values ('6','Mursan ','Terry ')
Merge #child as t
Using #parent as p ON (LTRIM(RTRIM(t.lastname)) = LTRIM(RTRIM(p.lastname))
AND LTRIM(RTRIM(t.firstname)) = LTRIM(RTRIM(p.firstname)) )
When Matched Then
Update
set PID = p.PID;
update #child
Set lastname=LTRIM(RTRIM(lastname)), firstname= LTRIM(RTRIM(firstname));
update #parent
Set lastname=LTRIM(RTRIM(lastname)), firstname = LTRIM(RTRIM(firstname));
select * from #child
select * from #parent
drop table #parent,#child