There have been quite a few inquiries about whether the name "Isaac" would be given to the area of disturbed weather currently located along the northern coast of the Gulf of Mexico, if it were to develop into a tropical cyclone. The short answer is no, it would get a new name.
Our analysis of the satellite, surface, and lower-tropospheric radiosonde data suggested that the disturbance we're cur...rently following originated within Isaac's broad circulation, but that it had its own surface pressure minimum distinct from Isaac's. This was perhaps most apparent late in the day on Monday, when the residual surface center of Isaac was located over western Kentucky while a second weak low was located over northern Mississippi and Alabama. Isaac's circulation continued to weaken after that and became difficult to track, while the new disturbance moved slowly toward the Gulf coast. So what basically happened here is that a little piece of Isaac broke away and moved south.
OK, now everybody get your lawyer and grammar hats on. The National Weather Service rule that applies here reads: "if the remnant of a tropical cyclone redevelops into a tropical cyclone, it is assigned its original number or name".
Notice the rule says "the" remnant, and not "a" remnant. This means that the storm's primary remnant (and not just any old part of it) has to re-develop in order for the name to be retained. Since the primary remnant of Isaac was still in Kentucky when the new low formed and broke away, the rule dictates that the new low is not entitled to the name Isaac.
This rule actually makes a lot of sense. If a storm died and each of two parts re-developed, we couldn't give the same name to both parts. Only the primary remnant would retain the name, while a lesser remnant or part would get a new name.