Says an apparent expert on names in Spanish (
http://onomastica.mailcatala.com/viewtopic.php?p=49#49)
that the name Aitana, which two users have described as Basque in origin, is not Basque at all.
The name comes from a mountain range in the province of Alicante. The mountains' name itself seems to come from the Iberian tribe which inhabited the region when the Romans arrived--they were the Edetanos, and their mountain was, Edetana. This form eventually became Aitana:
*Edetana>*Adetana>*Aetana>Aitana.
"Aitan" is a Basque word--it means father. But the use of "a" as a suffix to transform this noun into female would not follow the Basque language's norms. Similarly, it is not a variant of the Basque name Aintzane, which means Gloria. It is not a variant of the Hebrew name "Aitan"--nowadayws associated with Ethan--which has no female form.