The name 'Jane' originally comes from the Hebrew name 'יוֹחָנָן', or 'Yochanan', which means 'Yahweh is gracious', and has also come to be interpreted as 'Gift from God'.
Something a lot of people don't know about the name is that it's actually a feminine version of the man's name, 'John'. Many centuries ago, 'Joan' had previously been the main female equivalent to 'John', but it was eventually outstripped by the current 'Jane'.
It was very popular back in the 16th-19th centuries, with a number of famous people from history bearing the name, such as Lady Jane Grey, the Queen of England back in the 16th century; Nobel Peace Prize winner Jane Addams; and probably the most famous of all, the globally-beloved novelist Jane Austen.
The name also had a bit of a resurgence in popularity in the middle of the 20th century, especially in America, evident from the number of famous actresses and singers that were born during the 1950s and '60s, such as Jane Lynch (Glee), Jane McDonald (Loose Women), and Jane Krakowski (30 Rock).
In the past few decades, however, it's fallen a little out of favour among the general population, and unfortunately it tends not to make it onto the Top 100 Baby Names lists in the US or the UK. But that just means that people like you with the name Jane aren't quite so common, which isn't a bad thing!