I'm facing the same question. We are Odoo 15 (Odoo.sh).
Client is in Ireland. Test messages send successfully, but they deliver as coming from 'Odoo' as the sender.

I have a support case open, but doesn't seem that anyone can give me a simply straight answer.

What I know is that the Sender Name can't be configured in Odoo, it's part of the external sender/provider. Under IAP Service Settings, it appears I could register as sending service, but it's showing only for countries Kuwait and Saudi Arabia

If I get an answer from Odoo then I will update .... If I don't get an answer soon, then we will need to use 3rd party integration service with Twilio, which is a shame as I want to keep it all under Odoo services