English, Italian, Spanish: Sylveon
Japanese: ニンフィア Nymphia
German: Feelinara
French: Nymphali
Korean: 님피아 Nimpia

Sylphs are mythological spirits, most commonly associated with the element of air. Due to this, when Sylveon's name was first released during Pokémon X/Y promotions, it was speculated that it could be a flying/air type Pokémon, despite the -eon suffix that has been used for all Eevee evolutions. However, Sylveon's name clearly derives from the use of sylph to mean fairy, as first seen in the ballet La Sylphide (The Sylph).

A sylph can also refer to a slender woman or girl, similar to a nymph which is a nature spirit usually depicted as beautiful young maidens - much like how fairies are commonly shown in art. I find it interesting that Sylveon is such a stereotypically feminine looking Pokémon (it's cute, it's pink, and it's adorned with bows) when it's name refers to such feminine creatures in mythology and popular culture, especially when the gender ratio of Sylveon is definitely male dominated.

The (feminine) German word for fairy is fee, explaining Sylveon's German name. And as an English speaker, Feelinara also makes me think of Sylveon's feelers, giving the name dual meanings.