This Happens when two users upload a picture with the same name!
It displays the first picture uploaded with that name!
Any way that rsgallery can change always the name to something else to avoid that?

Let's start with some general information to see if what you experience is "just the way it works" or that there is an issue. Please read this first:
http://docs.joomla.org/ACL_Tutorial_for_Joomla_1.6

In RSGallery2 the Access Control is implemented analogous to the core Joomla components. This means that the systems for what users can view and what users can do are seperated:
1 - view access
2 - "do access": edit, create (upload), delete, (un)publish (and for RSG2 also Vote and Comment)

The first is done via different User Groups. When you view the details for a specific gallery in the backend (Backend > Components > RSGallery2 > Galleries > [Edit a gallery]), you see a setting "Access". That's the place where one User Group can be chosen and all users who belong to that User Group can view images in that gallery.

The second is done via Permissions, either via the Global Configuration, the Options screen of the component (Backend > Components > RSGallery2 > Control Panel > Options; these are the component level setting which are (partly) inherited from the Global Configuration settings, and finally at the gallery level (edit a gallery and you see the permissions when you're allowed to see them, these are inherited rom the component level).

The frontend upload/edit system of RSGallery2 (called "My Galleries") can be setup that users can only see their own galleries where they are allowed to upload images to and/or show only their own items. This is a permissions setting (what are users allowed to do), not an access setting (what are users allowed to see).

So depending on the view access settings of the galleries and what usergroup a user belongs to, users can indeed see the galleries/item of other users if they belong to the usergroup that is allowed to view a gallery.

Gallery thumbs in the gallery view, like shown on this page http://demo.rsgallery2.nl/index.php/demo-rsgallery2, are taken from the gallery itself or its subgalleries when a gallery is setup to show a random thumbnail as the gallery thumbnail. The site admin can also choose a specific thumb via Backend > Components > RSGallery2 > Galleries > [Edit a gallery] > Setting: Gallery thumbnail (default setting is a random thumb).

When testing I almost always use the same set of images, that means that I use images with the same name a big number of times. RSG2 does create new filenames for images uploaded with a name that already exists (e.g. test_150x600.jpg becomes test_150x600-1.jpg the second upload and test_150x600-2.jpg the third time, etc.). I'm not aware of any problems with that...

I think I understand and I would like to see this myself. Could you create a useraccount for me that is similar to the accounts that you make for your other users (and perhaps a second account with permissions to remove images that I upload and galleries that I create if your regular users don't have that permission?). You can PM me such details. (I'll be uploading images like in this gallery: http://demo.rsgallery2.nl/index.php/demo-rsgallery2/2-second-gallery).
Note: While I treat other peoples' sites with the caution I would expect from people using my site, I do assume that you have a full backup of your site and database!

Another few questions:
1 - What are the permissions for the gallery/galleries in which users upload their images? E.g. if you have this problem that user xyz upload an image to gallery xyz, what are the permissions of this gallery xyz for the usergroup(s) that user xyz belongs to? A screenshot of the permissions section might be easiest to show this.
2 - What are the permissions of this user xyz according to the Debug Permissions Report (see section "How to find out what the permissions of a user are?" in http://www.rsgallery2.nl/rsgallery2_3.x_bugs_problems/posting_rules_16708.0.html)

What you could always try first, if you think that the watermark may be the issue, is emtpy the /JOOMLAROOT/images/rsgallery/watermarked/ directory so that new watermarked images are created.