Currently, text messages are sent using a large pool of phone numbers. Therefore, members will usually receive text messages from a different phone number each time a blast text is sent out.
With the new pricing we announced, one of the benefits is that it'll allow us to develop functionality where we can assign individual phone numbers to communities, so that blast text messages come from the same phone number each time.
This feature request will be used to track our progress on this; give it an upvote if you're interested in following along!