I think Shania Twain named her SON Aja but I agree that it sounds quite feminine.
It does mean 'Goat' in Hindi but I found the following comments posted on a name site:
"Aja is an awesome name that means "Pretty One" in Korean and "Spirited One" in Swahili!" Of course I don't know if this is accurate or not.
"Nickname for Ajalon, where the sun and the moon stood still, as Joshua commanded."
"It is the name of my husband's favorite album from his favorite band, Steely Dan!"