Here are some sweet girl-name ideas formed from Akash and Shokhi (mixing sounds/letters) and also sounding nice in Indian/Jain families:

1. Akshi – from Akash + Shikhi
2. Akshika – extended form of Akshi, very popular and gentle-sounding
3. Ashika – from Akash + Shokhi; meaning “beloved / dear one” in common use
4. Akshita – from Akash; commonly taken to mean “indestructible / blessed”
5. Kashvi – from Akash; often taken as “shining / bright”
6. Akshiya / Akshiyaa – soft variation of Akshi
7. Shika / Shikha – from Shokhi; means “flame / peak” in common Sanskrit use
8. Akshika Shree – a double name; sounds traditional and graceful
9. Aksha – short, easy, modern-sounding, from Akash
10. Akshohi / Akshohiyaa – a more unique, direct blend of “Akash + Shokhi”

From a Jain point of view, you may like to choose a name that is easy to use with ‘Devi’ or ‘Jain’ at the end, and that sounds gentle and satvik when used in prayer or recitation (e.g., Akshika Jain, Akshita Jain).

If you tell me which style you like (very traditional / modern / very unique), I can refine this to 3–4 best options.