You can actually make a "tiny" url to the image by using the proper functions if that is what you mean. But maybe you just want a user friendly URL such as site.com/XXX/YYY. If so you need to be using mod_rewrite. There is an option for that, but maybe since it is apparently not set your server does not support it. (BTW, the "tiny" urls will not work without mod_rewrite either.)
I wanna make page of picture: http://site.com/album/image.jpg, where image.png - field to select from db, and i wanna replace it to ID: http://site.com/album/1
Not possible is of course meant as not without some programming work. It would be possible to filter the URL via a plugin and turn that link into the appropriate Zenphoto parameters internally.
But there would be some drawbacks--you could then never have an album where the name was simply digits.
Anyway, maybe a better approach to this is to describe what you want to accomplish. The URL you originally complained about is caused by not using mod_rewrite. If you enable mod_rewrite the links look much more friendly. Is that all you need to do or is there some intrinsic reason why the link needs to be a number?
Unless you enable mod_rewrite there is in fact no possible solution as there is no means of intervention by Zenphoto--all links must point to an actual file.
If you really want a link that looks like http://site.com/album name/# and your site supports mod_rewrite, a plugin can attach to load_request filter and provide the mapping.
As my colleague explain it is not that simple. The urls are generally created internally and not by mod_rewrite direclty.
As already suggested maybe explain first why you need to do this actually. I mean is the "images" really needed as naturally an album may contain those?
Please see: http://www.zenphoto.org/pages/paid-support
I should warn you that such customization does not come cheep. So if it is worth several hundreds of dollars for this feature make a request of one of the parties on the page.