This year, it asks me to complete this. It says if you are a single member LLC and have EIN, to list LLC and EIN.
I have always filed under my SS # and have always reported my rental income on Schedule E.
I did request an EIN last year, but haven't used it for anything.
How am I supposed to complete these questions to list owner (me) or LLC? And SS, or EIN?
Please see this answer from DS30.
You will use your SSN since this is a disregarded entity. This applies to your quarterly estimated tax payments as well.
However, you can use either your SSN or EIN when receiving 1099-MISC income. Just make sure to report all these 1099-MISCs under your Schedule C since they all relate to your LLC business income.
Also you can use your EIN for your LLC when necessary like if purchasing property for your LLC or filing your Sales tax report with your state's Department of Revenue.
For more information see Single Member Limited Liability Companies