For each API , there is a different error code that indicates that the sender is illegal or invalid for this message:
SMPP API - Rejection code 10 - "Source Address - Submission Control Failure"
REST API - Error code 15 - Illegal Sender
For messages to the US or Canada, the sender should be a virtual long number. If a different sender is submitted, the message will be rejected with the one of the errors above, depending which API is being used.
You can purchased numbers from within the Dashboard.