Macadia
Sensible. The phrase "next of kin" sounds like you've popped your clogs. I vote for "emergency contact".
(My phone has a setting called I.C.E. where you enter an in-case of- emergency number that strangers can view even if your phone is locked with a password).
I too was going to suggest adding I C E (In Case of Emergency) to the entry of the person to call (or people, as the first one contacted may not answer) I have three contacts named, in this order - my brother, who lives only one street away but whose phone is often switched off, my son who lives at the other end of town but who probably has his phone on, and my daughter who lives further away and would take longest to reach me, but is the one most likely to answer immediately.
Paramedics would look in your phone for an ICE number.