This is supposed to be the origin of my own name (Adrien), and I was rather disappointed in the meaning. So I did some more research, sort of. Now this is entirely speculative and I am no etymologist. There was a town in ancient Israel known as "Edrei" which is mentioned in the Old Testament portion of the Bible (written in Hebrew). With the Jewish people every name has a meaning and the meaning of "Edrei" is "Strong". In the Greek translation of the Old Testament (the Septuagint) the name becomes "Hadrianus". Considering Greek was a strong parent of Latin it seems to me that a more accurate meaning would be "Strong".
After a little bit of research (it was very little, actually) I discovered that Hadrian has a feminine form, Hadria. However, Hadria is a very rare first or surname, and is practically nonexistant, despite the charm it might hold.
In the contemporary English-speaking world "Hadrian" is unusable. I am of the United States, and know for certain that it will be viewed as unprofessional, pompous, pretentious, childish, and "kre8tiv" (made-up!). Be aware of those facts before you write anything in stone. Ponder the issues of "Will the name chosen aid my child's future career?" "Will s/he be wrongly passed due to a name?" "Will s/he be subject to mocking?" "Will I be thanked later in life for the name given?"
I beg to differ with Francesca. I, too, am in the U.S., and Hadrian would not be seen as anything she listed. I suppose some could find it a tad pretentious, but that's it. It most certainly isn't "kre8ive." Learned people in the English-speaking world (and most others) should know of Hadrian's Wall along with the emperor for whom it was named.
A welcome change from the popular name of Adrian. But I keep reading this name as Hadron. As in the Large Hadron Collider. I guess some folks would probably think that you're a science geek and named your child accordingly. Which is cool IMO! XD.