I know that I can not keep more than one of the same name on the ground but I would like to know if it is possible to destroy the active one to cast another equal
Not only is it possible, that's almost always how it's actually used. One that I, personally, frequently use is Ashiok, the
Nightmare Weaver. I'll have an Ashiok out and activate his ability (+2, -X, doesn't matter). Then I'll cast another Ashiok and sacrifice the first one. Then use the + ability on the new ashiok.
As ApothecaryGeist pointed out, sacrificing the duplicate legendary is a "704.3: state based action" which means it will be done *before* any trigger goes on the stack. "Whenever a player would get priority (see rule 116, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event. If any state-based actions are performed as a result of a check, the check is repeated; otherwise all triggered abilities that are waiting to be put on the stack are put on the stack, then the check is repeated. Once no more state-based actions have been performed as the result of a check and no triggered abilities are waiting to be put on the stack, the appropriate player gets priority" As I'm given to understand it, in the
Legion's Landing example, you'd cast LL and get the trigger. Then, you'd cast the second one. It would be sacrificed THEN it's trigger goes on the stack. Also, any abilities that trigger when a permanent enters the battlefield are put onto the stack *after* the creature is sacrificed.
Additionally, and this got my playgroup when we first started, as a state-based-action, you cannot respond to it. For example, lets say you have a Ghost Counsel of Orzhova on the battlefield and you play another one. You couldn't activate the ability of Ghost Counsel to blink it. State based actions cause you to sacrifice before anything can be done, and cannot be responded to.