Edit:

The problem it is just like this video

https://www.youtube.com/watch?v=GBAjdsh3b34

Original:

i noticed that my companion started making some annoying clicking noises and it won't go away. After some research I found that this happens, when the companion is on a workbench and you fast travel, making the noise attached to the companion, regardless of what you do.

For some lucky individuals you can restore it to normal by going back in the telling your companion to sit in the workbench that they were before the fast travel, after they move it will stop permanently, if it isn't it will come back after your next fast travel. Unfortunately I cannot remember when that occurred, so i have spent hours running around the map of fallout 4 trying to find possible workbench to my companion to sit to fix this problem. Since I'm here you might have an idea how it is going, It is very frustrating.

Ps:: If you are in the PC there is a mod to fix this.