Yes! There's two ways to give someone else an SOS Button.
You can remove your SOS Button from the Devices screen and give it away. The new user will need to use their own service. If they already have service, they can pair the SOS Button and go right into using it. If they do not, they will need to purchase a separate Wearsafe Tag SOS Button with activation. Older stock available through third-party retailers can be used for this, as long as the item you purchase says it includes a subscription.
If you want someone else to use your SOS Button as part of your own account, download the Wearsafe App on their smartphone, then add the SOS Button in the app as usual. They will be able to send alerts, and they will also receive notifications when any devices on your account start an alert.