The origin of Isis (pronounced "IY-sis) is actually Greek and means "throne." No one knows for certain what name the Ancient Egyptians called her. In hieroglyphics, her name is sometimes written as "she of the throne." The reason the pronunciation of her original name is so disputed is because hieroglyphics have no vowels.
Isis is the daughter of Geb and Nut, gods of the earth and the sky, respectively. In addition to being the goddess of nature, reincarnation, and magic, Isis is also hailed as the ideal mother. And like a good mother, she doesn't pick favorites. She loves and will listen to the prayers of slaves and aristocrats with equal attention. She married her brother Osiris (incestuous marriages were common in ancient Egypt, so their mythology is going to reflect that). When her husband was murdered by Set, she used her magical skills to resurrect him (interesting side note, she had to learn his "secret name" in order to do this). During his resurrection, they conceived their son Horus.
Isis had her own cult that was popular throughout Ancient Egypt. She was so beloved that after the fall of Egyptian civilization, she continued to be worshiped in Greece, Italy, Spain, Germany, Arabia, Asia Minor, and even Britain. No one knows precisely what rituals were done in these cults. We do know that both men and women could be priests, that they were considered healers, and that some spells involved braiding or not combing their hair (this last part comes from the Egyptian belief that knots were magical, an idea that still exists in Wicca). Small parts of the Isis cult survived the suppression of goddess worship by Christianity. Isadore for boys and Isadora for girls are both Greek names meaning "gift of Isis" that are still used today.
Something else survived that makes Isis especially relevant to the Yuletide season. Isis is depicted in artwork in many ways, but one of the most common is when she's shown seated on a throne nursing her baby son Horus in her lap. Here's an example on the side. Does that image look a little familiar?
To be fair, I never read the Bible. But I had a college professor in art history who did and she said that the number of passages that mention the Virgin Mary, Jesus' mother, could be counted on one hand. She just isn't an important character. So where does all of the artwork of Madonna nursing baby Jesus come from? Many historians believe that even as Christianity grabbed hold over Europe, people still wanted a female role model to look up to. So they constructed the scene of Madonna and Jesus based on the earlier images of Iris and Horus. The theory makes sense if you think about it. They're both "the perfect mothers."
In modern day Neo-Paganism, Isis still plays a vital role even though we don't follow the same traditions that the ancient Egyptians had. She was recognized by The Order of the Golden Dawn, the coven Gerald Gardner was in before he started the Neo-Pagan movement. Kemetic Wicca follows the Egyptian pantheon and constructs rituals from The Egyptian Book of the Dead. Many feminist-based covens like the Dianic Wiccans adopt her as their patron goddess.
Wider culture in general is becoming familiar with the given name Isis. So far, it has reached the peak of it's popularity in 2005 and #522 in the top 1000 baby names. As for it's variations, Isadore was last widely used in 1910's and reached #328. Isadora is the rarest; as long as America has had the top 1000 it's never appeared. Despite that there are a few well known namesakes. Isadora Duncan is the most famous, considered to be the inventor of modern dance. And then there's Lady Isadora, a successful Pagan singer-songwriter and musician who was one of the genre's early founders.
Well, I hope I've made a good argument that Isis is a wonderful, feminine-yet-strong namesake for anyone to have. As you can probably tell, I like Isadora a whole lot.
Sources:
http://en.wikipedia.org/wiki/Isis
http://paganwiccan.about.com/od/godsandgoddesses/p/Isis.htm
http://www.babynamewizard.com/namipedia/girl/isis
http://www.babynamewizard.com/namipedia/boy/isadore
http://www.babynamewizard.com/namipedia/girl/isadora
http://www.ladyisadora.com/
Image Credit:
found via http://ffffound.com/
http://www.magictails.com/abydos/images/egyptian statues/large/egyptian statue isis horus sml.jpg