A Taekwondo studio, or training hall, is called a dojang in Korean.
The word 도장 道場 dojang literally means ‘hall of the way’, with 도 道 do meaning ‘way’ and 장 場 jang meaning ‘hall’. The is a reference to the ‘do’ of Taekwondo, which means ‘way’, and signifies that Taekwondo is not merely a skill or a passtime, but a way of life.
A Taekwondo studio or training hall is not called a dōjō. ‘Dōjō’ is a Japanese word that’s used in Karate to refer to a training hall. Dojang and dōjō are cognates in Korean and Japanese, so the meaning is the same, but Taekwondo, being from Korea, uses Korean words.
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If you'd like to learn more about the Korean terminology used in Taekwondo, consider buying this book: Taekwondo Terminology. It contains an extensive dictionary of terms used in Taekwondo, as well as explanations on how to pronounce Korean words, and aspects of Korean grammar.