They didn't get there on name recognition alone. There's quite a bit of talent returning. In fact, due to budget, resources, recent success and the fact they don't have to compete against any other instate school for the rich talent pool in Louisiana (unlike the vast majority of their SEC mates), there is absolutely no reason why LSU shouldn't be at least Top 20 preseason every year.
And let's be honest, with the above advantages both monetary and lack of instate competition, they should finish Top 10 every single season. To not is a complete waste.