Business name for home pet euthanasia

Hello, I'm a veterinarian who is starting a business for home euthanasia during after hours for the times when people's pets require assistance at the worst time (6pm-6am Saturday and Sunday).

My original plan was to call this small business "Perth Home euthanasia," plain and simple but my friends believe it might be a bit confronting to those not comfortable with the word euthanasia. So we brainstormed some names and I wanted some opinions;

Final rest, Farewell with Family, Second Journey, Peaceful passing, Peaceful rest, Peaceful farewell, Running Free, It's time/ It's their time, Pet's relief

What do you believe sounds the softest for those starting the process of grieving?