동일 = the same, identical. (동일인 = the same person, 동일 사건 = the same case)
-시 = suffix for regarding something. (X-를 영웅시하다 = think of X as an hero (영웅))
So 동일시하다 means to regard something to be the same as another, and 동일시하면 is its conditional form, like "if you think of A as the same as B".
- 배우가 맡은 인물과 배우 자신을 동일시하다 = to see the actor's assumed character as the actor himself.
- 배우가 맡은 인물과 배우를 동일시하면 안 된다 = You shouldn't lump the actor's assumed character and the actor as one.