I think the problem here is the way these images are being added, and the method in which this happens. So when you paste an image into Jira, by default it uses a filename such as 'image.jpg'.
The problem here is that when you then paste a different image with the same name, Jira does not have the proper means to differentiate between two files with the same name on the same issue when trying to display that image inside a comment. Jira has to use a markup which tends to look something like this:
!image.png|thumbnail!
The problem here is how is Jira supposed to understand which file with that name is supposed to be rendered here. I believe that it is not technically overwriting the first image. The way to confirm this though would be to look at this issue through the Jira main site (not via the customer portal). I suspect that JSD Agents and Jira Core/Software users looking at this issue in the main Jira site will be able to see both attachments.
This is not as much of a problem outside of Service Desk. In Jira Core/Software issues, users can still see all the attachments on the issue under the attachments section. But for Service Desk, customers can't see images unless these are referenced in the comments via the wiki markup syntax.
There is an existing documented bug on this problem in https://jira.atlassian.com/browse/JRASERVER-2169.
I realize this is not an ideal solution, but I would recommend that if you need to attach more than one screenshot in the same issue of Jira, to instead save these as image files on your system first and give them uniquely different filenames before you upload them to Jira.
Since you cannot edit the filename of an attachment on an existing Jira case, this looks to be the only way to avoid this problem when it comes to Service Desk.
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