Do you organize address book by last or first name?

I write them down by the names i address them.

I create all healthcare entries beginning with the word Doctor, even if it is not a doctor. For example:  Dr. Eastside Radiology or Dr. Mountain Laboratory. This way all entries are under the letter D. 

You could try the same with Family as the first word in each entry. 

If you are not confident to remember all the relatives, why don't you use brackets?

For example, Anna Liam (Aunt)

I manage my address book like that. Name in alphabet order and remarks in brackets. 

Because it is difficult to remember everyone when you have a big family!

I alphabetize by last name including family.

Both, mine is big enough for double entries.  I also writ the connections -- aunt, grandmother,  friend,  store, vet, tax guy, etc. 

In my private address book, I usually add people by their first names, so "Anne" is under A. If I call someone by their nickname like I do my aunt "Poppy", then she's in the address book by her nickname under "P". 

Basically, you can do whatever you want.

It's much simpler just to list everyone by surname, rather than having to wonder, "Did I put my cousin Susie Linton under "S" or "L"?

There is no need to add "cousin" or "aunt".

All by their last name, then in alphabetical order of their first name. I never use titles such as “aunt” in my address book, I know who they are!