Leo is probably the most well used of all the astrological names, but it still might not be in everyone's taste. Thankfully, given the lion's popularity there are lots and lots of alternatives. I'm going to avoid the obvious Leo/Leonie/Leontine/Leopold/Leon/etc. They're great, but lion names are actually really easy to find without including them.
1. Aslan. Means "lion" in Turkish. There is also a famous fictional lion with this name.
2. Simba. "Lion" in Swahili, but may be too Disney for some people.
3. Leander. Derived from the Greek leandros meaning "lion of a man." In Greek mythology Leander is the lover of Hero.
4. Bast/Bastet. Most people know this goddess in her tamer domestic cat form, but in her earlier form she was a lioness.
5. Ariel. Hebrew for "lion of God." Also has a Disney feel, but most have no problem using this one.
6. Bacchus/Dionysus/Dion. The Greek/Roman god of wine and all manner of debauchery's symbol is the lion.
7. Lionheart. An eccentric choice, but it is historical. Richard I the Lionheart was a king of England.
8. Nemea. The Nemean lion was a vicious monster in Greek mythology that lived in a region called Nemea. It was eventually slayed by Hercules, and the lion became the constellation Leo.
9. Golden/Goldie. This is the color most associated with Leos.
10. Pride/Proud. A quality that is associated with Leos and lions in general (a family of lions is called a pride). It would be an interesting virtue name.
11. Regulus. The most famous star in the constellation of Leo
12. Sol. The sign of Leo is ruled by the sun, so any sun name will work.
13. Onyx. Other stones associated with Leo are Topaz, Carnelian, Ruby, and Tourmaline.