I applied with the name
Lucinda Snow
and was denied
Is it taken and if it is shouldn't it say that instead of your name is invalid?

"Snow" was probably your problem as it's a word not a name. You should try swapping out for another last name.

http://en.wikipedia.org/wiki/Tony_Snow

Tony Snow, the former press secretary of President George W. Bush. Seems like a perfectly reasonable name to me, and certainly not on the level of most others that get denied.

Nouns can be used as surnames, with a proper first name. So there is nothing wrong with the name itself but the rules do state you need permission to use an existing last name, there already being at least one Snow in SWC.

However I'm not actually sure to what extent we enforce that considering it relies on us recognising the name so most likely it was mistakenly declined or the wrong reason for declining it was selected.