You can change the public URL of your chart/infographic as you wish, even after publishing! Hit the Share... button in the top right corner of the editor and adjust your chart's title in the share panel – note how it changes the link at the bottom instantly.
Keep in mind that this doesn't change embed codes, and charts embedded with our embed codes will still work. However, if you have embedded your charts in a different way/using a public link, you will need to change it there too, or, better, use the "hard link" which is visible in our embed codes.
In other words, you can open one and the same infographic with this link: infogram.com/single-chart-layout-side-by-side-1g502yl531vdpjd or this link: infogram.com/8d5580b8-1a0e-4ada-8ba6-869d666ff8e9 and the latter won't be affected to renaming and won't change unless you choose to unpublish or delete your whole infographic.