I the US, obituaries aren’t required and in my experience it’s up to whomever is requesting it decides who and what is included. So it could be <deceased>, survived by <spouse> and <children>, <step-children>.
For my Dad’s obituary, in addition to my brother and sister’s spouses being listed, she insisted my live-in girlfriend be listed also because my Dad genuinely liked her. We had her listed a after my name (I’m the youngest) as “friend”. We all assumed she would be taken as my partner, but a few friends of my Mom thought she was my Dad’s girlfriend!
Edit: In Hawaii, it’s common to have hanai listed. Hanai can be anyone (though usually children), related or unrelated, but treated as an equal (son, daughter, uncle, aunt) by another family.