Now you can change your chart/infographic public URL as you like, even after publishing! Just hit the Share button in the upper right corner of the screen and adjust your chart's title at the top of the pop-up window - note how it changes the link name at the bottom instantly.
Keep in mind that this doesn't change embed codes and embedded charts using our embed codes will still work. However, if you have embedded your charts in a different way/using 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.