Pretty much everything within the Bubble has now been mapped, though there might still be one or two outliers out there somewhere. Noticed in my own perambulations that Guo Zi had a whole bunch of Unmapped planets in it a couple of months ago; when I posted this fact here on the forum, they were all gone within a few hours. Nearby, Bulkuylkana also had a few Unmapped planets in it, right up until it became a Control system for Yuri Grom. But I haven't seen any Unmapped planets in the past few months.
So if you want your own name stamped onto some poor unsuspecting planet, you'll have to leave the Bubble. Once you get out past 500 LY from Sol, finding systems with Unmapped planets becomes more and more common. You need to get out beyond 1000 LY before actual Undiscovered planets start to become common.
All depends on the direction you go, of course, The straight-lines to Sag A, Colonia, the Formidine Rift and all the big, shiny nebulae are thoroughly explored by now. "Aim at nothing", and you're more likely to find Unmapped and Undiscovered systems.