I had this problem for quite long time, but like with everything its just about taking small steps at the time. I for example started this in CSGO because I didn't really care about my rank or performance there so I didn't have pressure and I just started making simple info calls. Like "short one", "ramp one" etc. Just small info and eventually it got comfortable. And also I always try to think that good info is good for team, so no matter how you perform individually you can still have nice impact just by comming simple info.
Also playing with friends made me more relaxed in games and I had way easier time communicating. I'm still not super talkative in games or anything, but its way better than what it was before. Its just all about making small improvements here and there.
Also something that in the past has helped me was playing on alt account. There was just something about my voice "being linked" to my real account with real rank that made me even more nervous and also put more pressure on performing. So playing on alt account made me more relaxed. Just something you could try if you want.