Thumb /θʌm/
Index finger /ˈɪndeks fɪŋɡər/ (also first finger /ˌfɜːrst ˈfɪŋɡər/, forefinger /ˈfɔːrfɪŋɡər/)
middle finger /ˌmɪdl ˈfɪŋɡər/
Ring finger /ˈrɪŋ fɪŋɡər/
Little finger /ˌlɪtl ˈfɪŋɡər/ or pinky /ˈpɪŋki/ ( also pinzzkie) (plural pinkies)
They are all countable.
Note:
Sometimes, 'finger' doesn't include 'thumb'.
He held the beetle between finger and thumb.
We have two hands. How do we identify one specific finger?