Does each Region only have 8 gyms in Pokémon? I remember that at the start of the Pokémon the anime, Professor Oak said that there are a lot of Gyms across the region. You only need 8 to enter the Pokémon league, thus Gary have 10 gym badges.

However, no matter who I ask, no one seems to remember this or heard of this. I watched Pokémon in Chinese sub with Japanese voice. so did I remember wrong or something else happened?
No. The pickle Tickler has essentially lists the gyms from the games, which are correct. 
The Pokemon Anime however doesn't follow them. We know this because as you said, gary won 10 badges in the anime. And that is without the Earth Badge.
Hence there were ATLEAST 11 gyms in Kanto region.


  Alot of other characters in the anime like rivals have been shown with different badges that ash hasn't had. I this shows there are gym all over the region in the anime but you only need to defeat 8 gym leaders to enter the league. 


Ash, misty and brock have also met other non-game gym leaders in the anime like Dorian from the coastline gym in johto. Barry, Morrison and Trip have different badges too.

Also note, Candice says that not many people come north to challenge her. Does that mean only people that beat her go to the Sinnoh League? Ergo, Sinnoh has more Gym options too.

The reason Ash battles only the game Gyms is to reduce confusion and have people look forward to the other Gyms.

Source: Pokemon Badges: Anime Only Gym Badges

Gary's Gym Badges: Some Known ones
Otoshi's Gym Badges: most completely different than normal ones.
Morrison's 8th Badge
Barry's badges:3 Unidentified ones
Trip's Badges: Only the first 2 are from the games