Yes, the root of Hanuman (हनुमान्) is really hanumat (हनुमत्). As per vyakarana rules of Panini’s Ashtadhyayi, the word is formed by adding the मतुँप् (matum̐p) suffix to the word हनु (Hanu), meaning jaw.
Panini’s Ashtadhyayi gives the following sutra for the suffix:
तदस्यास्त्यस्मिन्निति मतुँप्॥ ५।२।९१
Meaning: that which belongs to him (or this) (...