It could be a jealous ninja from another village. This ninja has always been envious of Naruto's power and Hinata's beauty. When he sees their relationship growing, he spreads false rumors that cause Hinata to run away. He then tries to prevent Naruto from finding her so that he can take Hinata for himself.
It could be a rogue ninja who has a vendetta against Naruto and sees Hinata as a way to get to him. This antagonist might try to disrupt the relationship between Naruto and Hinata where Hinata wants Naruto to be dominant, for example by spreading false rumors about Naruto's methods of training Hinata.
It could be Neji. Even though they are family, Neji has been quite tough on Hinata in the past. His overbearing nature and the way he has sometimes looked down on Hinata could be the final straw that makes her snap.
It could be a future version of himself. If Dark Hinata travels back in time, his future self might see this as a threat to the timeline he has created and try to stop him. This would create an interesting internal conflict within the character.
It could be a time - traveling rogue ninja from the future who wants to change the past to gain power. This ninja might try to stop Hinata's mom from achieving her goals in the past.
Maybe it's a jealous rival of Naruto who wants Hinata for himself. He manipulates situations in such a way that Hinata ends up hurting Naruto. For example, he could stage events to make Hinata think Naruto has betrayed her trust.
One idea could be that Hinata runs away due to family pressure to marry someone she doesn't love. Naruto then sets out to find her. Along the way, they both discover new things about themselves and their feelings for each other. Maybe they end up in a hidden village where they have to work together to survive and in the process, their bond deepens.
It could be Orochimaru. He is known for his experiments with curse marks, and he might see Hinata as an interesting subject to study or use for his own evil plans.
In this fanfiction, it's possible that the main antagonist could be an old rival of the Little Giant. This person might see Hinata as a threat because of his association with the Little Giant. They could try to create problems for Hinata during matches or training, like spreading false rumors or trying to psych him out. However, Hinata, with the inspiration from the Little Giant, would overcome these challenges.
It could be a rogue ninja who has a vendetta against their village. This ninja might see the girls as easy targets or as a way to get back at the village. He could be tracking them down during their run - away journey.
Maybe a new character could be introduced as the main antagonist. This character could be from a hidden village that has been secretly observing Naruto's growth. They realize his potential as a weapon and plan to steal his power or use him to start a war against other villages.