익숙해지다: You get used to something (at your own will) 익숙하게 되다: it happened more or less regardless of your will/wish. (you end up getting used to something) ~게 되다 is something the subject doesn't have any influence on. eg: 선물을 많이 받을 거예요 the sentence above isn't grammatically wrong, but it doesn't make any sense because you can only receive as many gifts as people give you. And most of the time, you have no influence on that. Therefore, "선물을 많이 받게 될 거예요" is the correct version. I hope you recognize the difference now.

익숙해지다 > 익숙해 + 지다 > 익숙하다 (adj) + 지다 = 익숙해지다 (verb) 익숙해지다 > get used (active) e.g.) 운전에 익숙해지다. 익숙하게 되다 > 익숙하다 + 게 + 되다 익숙하게 되다 > become accustomed to (passive) e.g.) 현지생활에 익숙하게 되다.