I have my Advance Directives/Living Will Registry card in my wallet so my emergency contact (father) and papers can be accessed by anyone. My “what to do if I die” letter is on the computer my father can access.
I can only think of 2 friends who are not married, and they are brothers who live in the same house. That would be easy!
The distribution of single people by ageis an inverted bell curve, especially for women (Note: the chart shows the opposite - % of people married by age. To view the inverse, stand on your head). It’s higher at the younger end due to less opportunity and at the older end due to spousal death. Parents may be a good contact for many on the young end, but not so much the older ones…
The few single friends I have are people who are part of a circle of mutual friends. So even though there are a couple for whom I could not identify next of kin, there are others in the circle who could, even if I didn’t have the assistance of Facebook. I don’t think this would be a huge concern for me.
That reminds me, I have a “My Dog Is Home Alone” card in my wallet with my best friend’s name/number on it (and there’s a small tag on my keychain that points people to the wallet card). I guess I care more about making sure my dog gets taken care of than anyone being able to notify someone about me. 
Virtually everyone (except me) has a cell phone. Switch on the phone and start automatically dialing numbers, until you get next of kin.
All modern cellphones are lockable and many people keep theirs locked. If so, a Samaritan or responder isn’t going to dial anything until they provide a fingerprint, PIN, or similar. As a consequence, many phones provide a way to have the locked screen display a message like “In emergency, call wife Jane at 123-456-7890”. It’s still up to the phone’s owner to have turned this feature on and filled it in. And whoever’s helping will have to use their own phone to make the call. Which, given that so many people refuse to answer calls from unrecognized numbers, means the helper will be leaving a rather portentous voicemail that may or may not get listened to any time soon.
Yet another really nice thing we could all do for each other ruined by spammers.
Then there’s the double suckitude of a car with a couple in it who’re both badly hurt. So they find one victim’s phone and call the emergency contact number displayed. Only to hear the other phone ringing somewhere in the crunched up car.
In every case except two, yes I do know the next of kin. As for the other two as far as I know they have no surviving relatives and I have no idea who they consider close enough to call out in a will of any form. Heck, it could be me – I just don’t know.
I’d tell my wife and she would track people down.
From the office, HR should have instructions on your next of kin, including an attorney or other designated key point of contact.
From the family/personal life, your attorney or other designated next of kin should know how to reach out to the office world/HR only.
I don’t understand why you might need a service to handle this, but perhaps if it is that complicated, your work is best qualified to help you make those arrangements.