It would help if we knew what fields you have available on update or delete, but here I will assume you have al the fields in the user table.
Create Procedure ProcUpdateUser()
update user set name=@name where log_id=@logid
update login set username=@name where log_id=@logid
Create Procedure ProcDeleteUser
delete user where name=@name
delete login where username=@name
You will need to change the parameters according to your needs but hope this helps.