Electra was the name of three women: the daughter of Atlas and Plei'one, the daughter of Oceanus and Tethys, and (probably the best known) the daughter of Agamemnon and Clytemnestra who is the heroine of two well-known tragedies, respectively by Sophocles and Euripides.
Her name conjures up 'electric', of course, but this is merely coincidental (although etymologically justified), since it really means 'amber' (electron) or, possibly, the word of which this is a derivative, 'the beaming sun' (elector). Exactly why this famous name should have the meaning it does is something of a mystery. We know that the Greeks valued amber highly, but the precise link with any of the Electras mentioned here is not clear.
Perhaps the name is purely a 'bright and shining' propitious one. Stesichorus, a lyric poet of the fifth century BC, suggests - perhaps not all that seriously - another derivation. He takes the Doric form of Electra's name, Alectra, and makes it mean 'unmarried', from a-, 'not' and lectra, 'bed', that is, someone who is 'unbedded'.
But he may have been echoing what another poet, Xanthus, had said two centuries earlier, when he pointed out that Agamemnon's daughter was originally called Laodice but had her name changed by the Argives as for a long time she was not married.