Is it possible to label the messages we send using our own brand / company name?
Of course.
The ability to achieve this depends on which route you use to send your messages and whether your messages are associated with a subscription service or not.
If you are sending your messages using Global I, then all you have to do is key in your desired originator at the time of broadcast. This type of originator is known as dynamic and more information can be found here.
If you are sending your messages using Global II, then you must purchase the originator(s) that you would like to use well in advance and key them in exactly as they are registered at the time of braodcast. This type of originator is known as static and more information can be found here.
The originator of messages associated with a subscription service cannot be customised as it is used to provide recipients with the reply number used to control their participation in the service.