Sometime in 1801, Charles Hatchette, a chemist was analyzing a heavy black material from the rock collection of the then governor of Connecticut. He realized he had a yet unknown element in the room and called it Columbium - a name people use to refer to niobium even today (the official name being niobium.)
A year later, in 1802, Anders Gustaf Ekeberg was investigating two samples (one from Sweden and another from Finland) and found the same previously unknown element in both samples. He named it tantalum. There are two theories as to why he chose this name. Both of them are related to the myth of Tantalus so let's dive right in.
The Myth of Tantalus
Tantalus was born of Zeus and Pluto. He visited Mt. Olympus frequently and was on pretty good terms with the gods. Even after he stole ambrosia from them on more that one occasion. They tried to make him realize the error of his ways but oh no he paid no heed. Lets take a moment to acknowledge the weirdness of Tantalus here because what he does next will disgust you at least a little. Even if you're into cannibalism. Because there's a way to do things. So he invites his dear friends - the gods to dinner. And what does he serve? The obvious answer is he kills his son (Pelops) and cooks him till medium brown and serves warm. Right? (Actually, he serves him in stew, cut up in pieces according to some sources. Getting too graphic for you?) It isn't really clear why he does this. Maybe to test the gods or something of the sort. But they realize this and decides they've had enough of this very hospitable man. Zeus kills Tantalus pretty painfully and then takes him to the underworld where he is made to stand in a pool of crystal clear water. A fruit tree stands nearby. What's so bad about that? Well whenever he tries to drink the water, it magically recedes. When he tries to pick one of the luscious fruits from the tree, the branches would move just a little out of reach. Thereby condemning him to eternal hunger and thirst. If this wasn't bad enough, there was a huge boulder hanging precariously above him. It swayed every now and then threatening to crush Tantalus below. It never really falls so he has to live through eternal terror too.
Why is tantalum called tantalum?
As I said before, two theories. One, (the lame one - but it exists nevertheless) that Gustaf Ekeberg found the experience of discovering a new element 'tantalizing' for same reason. And the other - my favorite - that tantalum is so nonreactive that even when in excess acid it doesn't react. Really insoluble. So like Tantalus, even with so much water/ acid, it is unable to drink it (react/dissolve)
The Separation of Tantalum and Niobium
In 1809 William Wollaston proposed that columbium and tantalum were in fact the same material. Their striking similarities in both physical (shiny, grayish, hard - soft in the pure state though) and chemical properties (extreme unreactivity) didn't make this hard to accept. And that's what people came to believe. For thirty five whole years.
It was only in 1844 when Heinrich Rose showed that although columbium exhibited both the +3 and +5 stable oxidation states, tantalum showed only the +5 state that this misconception was remedied. He renamed columbium as niobium after Tantalus' daughter Niobe. This was because niobium was often found present associated with tantalum in tantalite ( an ore of tantalum with iron).
It was only in 1844 when Heinrich Rose showed that although columbium exhibited both the +3 and +5 stable oxidation states, tantalum showed only the +5 state that this misconception was remedied. He renamed columbium as niobium after Tantalus' daughter Niobe. This was because niobium was often found present associated with tantalum in tantalite ( an ore of tantalum with iron).
It was still pretty hard to separate Niobium and Tantalum though, because of their very similar properties. So it was a breakthrough when around 1866 Jean Charles Galissard de Marignac discovered that both these elements could be separated by fractional crystallization of potassium heptafluorotantalate (K2TaF7) and potassium oxypentafluoroniobate mono hydrate (K2NbOF5.H2O) This was a really good method to use because the fluoride of niobium is much much more soluble that the tantalum one.
Columbium and Niobium
Although Columbium and Niobium were shown to be two distinct elements a not very long after, both these names were used to refer to the same element for almost a century until the IUPAC officially named niobium niobium. Some people still prefer columbium. A lot of them Americans because the name columbium was thought of because after all, Charles Hatchette did get his niobium sample from America.