Can uploaded files be renamed in the server to avoid name collision? I want my site to host some images. The user is able to upload images as a content type.

If two users create content and upload images with the exact same name (myImage.png), will the older image file be overwritten in the server (and therefore both content entries would end up with the same image file)?

If yes, it is rather troubling. So now I wonder: is there a module that renames the uploaded file so it will not collide with other uploaded files?

I have searched for a couple ones, not exactly tested them since they seem to add too much extra functionality I just don't need: I like the default file uploading system that comes with Drupal 7. I just want it to avoid name collisions (if it happens).
You don't need to worry about the renaming of the images; Drupal does that for you by default :)
Lets say if you upload image1.jpg, and again someone else does the same the second file will be renamed image1_0.jpg.