It varies from deaf person to deaf person how they “hear” their inner voice. It depends on their level of deafness and vocal training. Those who were born completely deaf and only learned sign language will actually think in sign language.
They see themselves signing in their head as they “talk” to themselves. However, deaf who have had vocal training will sometimes think in the sounds they’ve been taught to make when speaking to themselves. Recent research as revealed that language is interwoven in brain functions like memory, abstract thinking, and self-awareness.
Language tends to drive much of the brain’s core “hardware.” As a result, deaf people who are not taught at a young age sign language or never taught at all will be handicapped even though there is nothing wrong with their brain. They’ll stay mentally handicapped until they are taught a structured language.
Learning a structured language is essential at a young age due to how the brain develops and matures. A person who learns to sign later in life will carry learning problems with them for the rest of their life.