Yes, this can be done in certain countries. Unfortunately, countries like the US are not supported.
To check if is going to be possible to change the 'From' name, please send a test SMS to yourself (if you are in the relevant country) and see if the SMS ID appears on your phone - it would display as 'Sendible' as opposed to a number if this is supported.
If you would like us to change the name, there will be a one-off charge of $85 or £85 or 85 EUR (dependant on the currency being used to charge for your plan).
So that we can process this for you, please submit a support ticket with the name you'd like to use and confirmation that you're happy for us to charge the one-off payment to the card on file.
Please note: the name provided needs to be less than 11 characters long.