Do you mean you want to save them in a specific folder other than the default /Uploads/ folder (/categories/) or in a specific name (/imageX.jpg)?

OK, this might seem a not so simple solution, but in the end: it is pretty easy.

First a small explanation:
Most likely you're using a field from the type ImageField. This can be found in sapphire/forms/ImageField.php
If you open that, you'll see it's a subclass of filefield (ImageField extends FileField). This means: it's using all the features of sapphire/forms/FileField.php unless those features are overridden in ImageField.php

Well... what the SilverStripe devs are doing, can easily be done by yourself (avoid messing around in the core)

1) Make a new folder in the mysite-folder, for example: mysite/formfields/
2) Create in that folder a file like myImageField.php
3) Write in the first two lines:

4) Now look in ImageField.php and FileField.php if you can find a place where the defaultfolder is set. It happens to be in FileField.php with the following line of code (line 64):

5) Copy that line to your myImageField.php -file and paste it in there. Replace 'Uploads' with 'Categories'.
6) Close everything with these two lines:

7) Instead of calling new ImageField in mysite/code/Categories.php, you should now call new myImageField.
8) Don't forget to run a /db/build

That should be all.

BTW: I have never tried replacing the default-folder. However I changed the allowedMaxFileSize and that worked fine.
If it doesn't work, please post it here.

It's worth a try. And if it doesn't work, some kind of method could work.

I'm not sure though if I would use the URLSegment.
The nice part of the ImageField is that you can reuse images. And my suspicions are that they won't move into another folder if you reused an image from let's say the About-us page on the Contact-us page. So in that case the logic of the image-part of your assets-folder would get a terrible mess (let alone the number of folders you could get)

Ordering them dynamic by ClassName sounds better to me. But I would prefer it more or less hardcoded by function (banner, sidebar etc) or just a plain Images-folder.

By the way: whatever you are planning, I would test it with a hardcoded Images-folder before I would start any coding. Remember: I didn't test it myself.

If this is on your custom page then you have defined a custom getCMSFields() to add the image field. You can pass the folder name to this image field and it should use that dir rather then the built in one.