Is there any significance to the character names in Elfen Lied, particularly with regards to the more important characters? With some characters, there's a clear "meaning" - e.g. Nana, who was also known as "Number 7" at the research facility. Could other character names e.g. "Lucy" be allusions to something, or perhaps in some other way meaningful given the plot?
Although this is never confirmed it does fit the plot in a way
Lucy's name closely resembles Lucifer considering that Lucy is the evil alter-ego it would be one of the most fitting.
Another possibility would be that the name is related to St. Lucy/Lucia, but this is a pretty far fetched theory.
They threatened to drag her off to a brothel if she did not renounce her Christian beliefs, but were unable to move her, even with a thousand men and fifty oxen pulling. So they stacked materials for a fire around her instead and set light to it, but she would not stop speaking, insisting that her death would lessen the fear of it for other Christians and bring grief to non-believers. One of the soldiers stuck a spear through her throat to stop these denouncements, but to no effect. Soon afterwards, the Roman consulate in charge was hauled off to Rome on charges of theft from the state and beheaded. Saint Lucy was able to die only when she was given the Christian sacrament source
Edit Re-reading the related question What's the significance of the 'w' finger position in Elfen Lied? I think the st Lucy/Lucia theory is less far fetched then I thought myself. Elfen Lied seems to be pretty Christian influenced.
One other interpretation is that Lucy is a reference to the hominid, as mentioned by ninjalj. This would seem to make sense given the role of Lucy within the plot as a mitochondrial Eve for the researchers. However, the manga itself doesn't seem to explicitly explain why Kaede is designated as Lucy by the researchers, and so it isn't clear what the "correct" interpretation of Lucy's name (if there is even any) is.
The same appears to go for many of the other characters, beyond very obvious cases such as Nana.