In the Arab world it is very common to use the term ‘ain’ – eye – applied to love and affective issues, just as in the case of the Spanish expression ‘la niña de tus ojos’ (the pupil of your eyes) to describe someone specially beloved. It seems that the Basque name Ainhoa, whose etymology is not well studied, would come from the Arabic ‘ain el hawa’ – the eye of love -.
For this reason the name has retained the interposed ‘h’.
In the al-Andalus period it was very common that the emirs and caliphs took Basque and Galician wives and concubines, and gave their favourite ones this kind of nicknames.