From whom do I need to get permission to give a deceased person's name to the temple? Is there a hierarchy of relatives I need to ask before I submit records for my own ancestors?

Yes, there is.  In order to submit names to the temple, you need permission for the closest living relatives.  This is really important, so don't skip this step:

The order is as follows:
1) spouse
2) children
3) parents
4) siblings

Do not bypass this order.  If the spouse says no, the answer is no.  Do not go and ask the children.  If all of these are no longer living, you are free to do the temple work, so long as they have been dead for at least one year.

You have a responsibility to submit the following relatives:

1) Immediate family members.
2) Direct line ancestors


You MAY submit the following:



1) Biological, adoptive, and foster family lines connected to your family.
2) Collateral family lines (uncles, aunts, cousins, and their families).
3) Your own descendants.
4) Possible ancestors, meaning individuals who have a probable family relationship that cannot be verified because the records are inadequate, such as those who have the same last name and resided in the same area as your known ancestors.

You MAY NOT submit the names of persons who are not related to you, including names of famous people or names gathered from unapproved extraction projects, such as victims of the Jewish Holocaust.  This is absolutely unacceptable and can jeopardize the Church's relationship with other religions and our ability to use those names at all, even if we are related to them.  Do not put those soul's ability to receive the saving ordinances in jeopardy. There is order to everything the Lord does, and He will not forget them, and will take care of them in due time.  

You may submit the names of individuals with whom you shared a friendship. This is an exception to the general rule that members should not submit the names of individuals to whom they are not related. Before performing ordinances for a deceased individual who was a friend, you should obtain permission from the individual’s closest living relative.