What is the name of the ancient language of Hindu scriptures?

The ancient language of Hindu scriptures is Sanskrit, especially its early form, Vedic Sanskrit.

The Vedas, Hinduism’s oldest scriptures, were composed in Vedic Sanskrit and transmitted orally for centuries before being written down. Exact pronunciation was treated as crucial, so specialist recitation traditions preserved the sounds and sequences of the texts with elaborate memorization techniques.

Later Hindu works use Classical Sanskrit, the highly standardized form traditionally associated with the grammarian Pāṇini. Sanskrit became the language of major philosophical, religious, poetic, scientific, legal, and dramatic works across South Asia. It was also used extensively in Buddhist and Jain intellectual traditions, so it was not exclusive to Hinduism.

Sanskrit is an Indo-Aryan language within the Indo-European family. It has been written in several scripts over time, including Brahmi-derived scripts and Devanagari. A common mix-up is treating Sanskrit as a writing system: Sanskrit is a language, while Devanagari is one script used to write it.