While Elena (el-AY-nah) is having a moment in the sun, her sister Elina (el-EE-nah) is just outside of ranking. In 2015 Elina was given to 248 girls, a triumph considering she was only given to 5 girls in 1900 and no more than 13 until 1976. It wasn't until 2005 that she jumped past 100 births, so by all means Elina is still quite a rare gem. Elena, on the other hand, was given to 2,877 girls in 2015, ranking at #106. Similar-sounding Eliana (el-ee-AH-nah) currently ranks #103, given to 2,956 girls in 2015. If the baby name Eliana or Elena is perfect for you but you're afraid it's too common, give Elina a chance. She's streamlined and sophisticated, and truly sparkles.
Elena is the Latin cognate of Helen, from Greek mythology. The name most likely means "torch," with attention to the flame. Helen (Helene) was the daughter of Zeus and Leda, and her kidnapping by Paris ended up causing the famous Trojan War. Throughout history she's been known as the beauty that "launched a thousand ships." Elina is the Finnish and Swedish form of the name. Eliana, though only one letter off, is not related, but it is almost identical in imagery. Eliana is the Italian, Spanish and Portuguese modern version of Aeliana (Aelia is an alternate form; they are pronounced AY-lee-uh and AY-lee-ah-nah), from the Roman family name Aelius, from the word helios, meaning "sun." So, all bright flames of names. I'd also like to mention that in Greek mythology Helios was the personification of the sun. (And in Sailor Moon he was a Pegasus, but let's not go there! ;p)
If you want something even more rare, try the Old Provencal form of Eleanor, which is Elladine (ELL-uh-deen). (Also, Elatine, an aquatic plant, has a lovely sound.) Elladine saw 5 births in 1924 which may have been a creative combination of Ella and Dean, or the rare French version. Something rare and very similar in sound to Elina - Elisena (ell-ee-SAY-nuh). which is a plant and also a princess character from Amadis de Gaula. It is likely a variant of Alison, meaning "noble character." Neither Elladine nor Elisena were given in U.S. record, or at least less than 5 were born in any given year.