Where is the message center on Moto G? I have a Moto G and I am not able to send messages, not able to find message centre. Where is the message centre?
Summarized from Motorola forum, Moto G and Moto X are designed in such a way that it will take the message center number automatically from the Saved configuration of the SIM. Try changing the SIM from Slot 1 to Slot 2. Save and set as default for newly received configuration settings.

You can try the following method by SmaRkieS on Android Geeks:


  Dial *#*#4636#*#*.
  
  You will get a menu. From that, select Phone Information. You will find
  a setting "SMSC". Refresh it. It is most likely to retrieve the
  message center number from your operator (or call your operator, and
  get the message center number, and then update in this field), then the
  problem should be resolved!