I recently had the same issue with my most recent Motorola purchase.
Everything worked on initial setup except for my messaging app, which could send but was unable to receive messages.
I have been with my third party carrier (and the same SIM card) for 6 years. The first suggestion I was given was to put in an updated SIM card - but I could not get cooperation from my carrier in sending me one. If you are currently with a carrier that is supported by Best Buy they will replace the SIM card for you in store free of charge.
The resolution that worked for me was to factory reset my phone. Had I known to do this immediately - it would have saved me so much stress and hassle! I immediately got the full backlog of text messages that I had not been receiving in the two weeks prior to the reset.
I would definitely recommend trying this if you are experiencing the same issue with your Motorola phone on initial setup!