The issue to stop without finishing the Pasuk would be that you are creating an ending for a pasuk in a place where Moshe Rabbenu didn't end it. The Chayei Adam (5:2) , with the interpretation of the Chesed Leavrohom (216) and the Tzitz Eliezer (12:40) , writes that this is only an issue if you would intentionally do so, but if your intention is to complete the pasuk differently (in a case where you only repeat the second half of a pasuk) or in a case where you repeat the full pasuk without first completing it (if the mistake was in middle of the pasuk and the reader goes back to the beginning before the completion) then this issue doesn't apply. The Chayei Adam explicitly says that this is the case even if the Shem Hashem is repeated.
The Tzitz Eliezer concluded that the prevalent custom is that if a mistake was made after the shem hashem was said, the pasuk is completed and only then repeated. But if there is another Shem Hashem still coming up in the pasuk, one should apply the heater of the Chayei Adam and stop at that point (prior to the next Shem hashem) and start over
For further reference -הקריאה בתורה והלכותיה , עמוד קסט