Hi, and welcome!
First of all, yes, you would still use 15s. That number refers to the diameter of the needles, so if you are converting from dpns to straight to circulars, etc., you would use the same number to keep the same gauge, meaning, the same stitches per inch, so that your project comes out at the size intended. The only thing is that if the needles are made from a different material, that can affect the gauge. So let’s say you’re getting 2 sts per inch with metal needles size 15. But if you switch to plastic size 15, that might make it 2.5 sts per inch, even though they are the same diameter. The different materials will grab the yarn differently and change the size of your stitches.
Now, as puddinpop said, if you are only casting on 6 sts, it would be impossible to use a circular, in the usual way (see below). When you use dpns, you ARE knitting in a circle, but you would put 2 sts on each of the 3 needles (and then work the sts with the 4th needle). But on a circular, the sts have to sit comfortably on the entire length of the needle, which is the length of the 2 needles plus the cable in between. The one exception to this, is a technic called Magic Loop. I don’t use it, but there should be a video on this site for it. So I don’t know if you can do it with such few stitches, and I know you have to have a fairly long cable for it. How long is your circular needle. And what are you making?