How can I separate sodium ions from brine or molten NaCl?
You can't simply produce isolated sodium ions, you also need to have an equivalent amount of counter ions of the opposite charge. So, in this case, you are going to get sodium chloride unless you introduce some other negatively charged species.

So you could just evaporate water which will give an increasingly concentrated solution of sodium chloride and, eventually, solid sodium chloride (which will contain all your sodium ions alongside an equal number of chloride ions.

This sort of separation is commonly used for a different reason: to produce pure water. Sea water is too salty to drink but there is far more of it than fresh water. So distillation (retaining the fresh water) or reverse osmosis (which produces more concentrates salt on one side and fresh water on the other). These techniques produce both fresh water and more concentrated salty water (which is one way of getting more sodium ions in your product).