The 1968 film "Isadora" about Isadora Duncan, the dancer
Isadora, which can also be spelled Isidora, is a Greek and Latin name meaning "gift of Isis" and the feminine form of the boys name Isidore, from Isidoros. Isis was the main goddess recognized in Egyptian myth, and although Isadora would be considered a pagan name by Christians at the time, it survived their repression, even becoming a saint name. Isis has currently fallen out of the top 1000 due to the terrorist attacks by the Islamic State of Iraq and the Levant, inappropriately shortened to ISIS when "Levant" is substituted for "Syria." Within going on a rant about how it should have stayed ISIL to save the children who already have this first name from being accosted or bullied, I will simply say that because no one wants their newborn associated with this group, usage has come to a halt. It is unfortunate because Isis was a great and peaceful female deity and the children who helped make Isis get onto the top 1000 will now suffer. So, parents who wanted to name their baby Isis, take note of Isadora/Isidora!
The second syllable of Isadora is what means "gift," from the Proto Indo-European root word deh-. Other names, such as Theodore and Pandora share this root. Isidra (ee-SEE-drah) is a Spanish form of this name, usually only seen abroad but given to a handful of girls in the U.S. every once in a while.
There were a few St. Isidore's and a Saint Isidora, but the name Isidore was often shared/unisex, especially during the Middle Ages when this was common. Saint Isidora was a nun in an Egyptian convent, and by records was one of the most humble saints. There are dozens of male and female historical namesakes, including religious leaders, philosophers, theologians, geographers, architects, poets, composers, writers and dancers. Isadora Duncan was the late American dancer with a tragic story worth reading about if you're considering this name.
In 2015 Isadora ranked a bit outside the top 1000 with 169 girls given the name, the highest amount in record, and Isidora ranked much lower with only 20 girls given the name (25 in 2007 was the most recorded). It ranked on the top 1000 for a total of five years between 1880 and 1900, but fares much better in Chile as a top 10. Isadora is rising in popularity as an Isabella alternative. The male names Isidoro and Isidore are not popular at all. In 2011 only 7 boys were named Isidoro and 7 named Isidore.
Izzy, Isa, Isis, Dora or Dory? Take your pick. *Update: Sadie, from the comments.