I reread your original post above, let's clarify a few points,
201-555-1212 - This is the "Caller ID" field.
DOMINOS PIZZA - This is the "CNAM" (Caller Name) Field.
Via an Obi, GV only supplies the Caller ID field, never the CNAM field. So you will always see a blank or something like "Unknown Name' or whatever in the CNAM field.
Back to your original question. If the Obi Call History is showing a number for the Caller ID field, then your phone (between the first and second ring) should be showing the same thing. If this is not the case, then determine why, ... is phone set to NA (North America) ring/caller ID standards, have you changed any Obi ring or caller ID settings away from NA standards (defaults), is your Obi a NA model, etc.?
P.S:, For the record, there is a workaround to get CNAM with GV on an Obi, you use a second SP slot, forward incoming GV calls to it, it adds CNAM, explained
here.