Neither the email verification template nor the SMS verification template can be modified. You can select the language from the Firebase console, however, this is a per-project setting and you can't modify the templates.

We understand that changing the template would allow you to tweak the user experience of your app, but we don't allow this to prevent abuse of the service. Update 1 year later, still a no go, but I received this back from support

The Firebase SMS Authentication message content will depend on the platform you are requesting that message from. Here is a list of the possible variations you may get:

iOS and Android - The SMS messages draw the app's name from the App Store / Play Store. One app is published, the correct name should start appearing. There may be a small delay (a week or two at most). 

Web - It will always use the domain that the SMS is requested from. To modify it, you can set up a custom domain.

iOS (using Recaptcha) - Phone authentication on iOS will show the project's URL instead of the app's name in the verification SMS when using the reCAPTCHA flow. This is the expected behavior. The reCAPTCHA flow was added for cases where an APNS token is not available (including on real devices). If APNS is not correctly configured, a real device will default to the reCAPTCHA flow.

Unfortunately, neither the email verification template nor the SMS verification template can be modified. You can select the language from the Firebase Console, however, this is a per-project setting and you can't modify the templates.

We understand that changing the template would allow you to tweak the user experience of your app, but we don't allow this to prevent abuse of the service. I hope this clears your consults about this topic. If you happen to have any more questions, please, do not hesitate to write back!