I already have a SIM card with a company that allows tethering and A2P.
I want to be able to send an SMS with a unique sender ID (company name) using that sim card.
Is this possible and if so, what should I purchase and how do I set it up?
It is NOT possible to alter the senderid when sending SMS using a SIM card + modem. The senderid will simply be the number belonging to that SIM.
If you want to have a custom (alpha) senderid, your only option is using a professional A2P SMS gateway. But even then it is not always possible, as not all countries allow alpha senderids. They might get overwritten to a short/longcode, or the operators require senderid whitelisting (basically, you need to request "access" to an alpha senderid, by sending your personal/company details and SMS content details to the operators. This is done to battle SPAM messages)