It is implied that proximity to the Crack was necessary for the answer to be heard.
Though it wasn't outright stated, the presence of the truth field implies that answers have to be pretty close to the Crack in order to be heard. I suspect the Doctor was bluffing when he claimed to be able to summon the Time Lords from aboard the Mainframe ship.
Beyond that however, only by being immediately nearby could the Doctor know in time if something was happening to Christmas which would warrant his needing to say his name. If he was too far off, he couldn't be sure of responding quickly enough--time machine or no.
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