Since this issue has reared its head with every version of windows I can remember, there's not much rhyme or reason to it.
I know it doesn't make much sense, but, for me, I have found it has something to do with 2 things...where my Recycle Bin icon is located on my desktop and whether I'm dealing with a folder as opposed to a shortcut or file.
As long as Recycle Bin is positioned in the first position in upper left corner of the desktop, everything seems to work as expected. If I send a shortcut to the desktop or save a file to the desktop, it will always go to first vacant spot reading top to bottom on left side of screen as expected. If I drag that shortcut or file to where I want it, it stays where I put it. Likewise, if I manually create a shortcut or file on the desktop, it will stay at the position clicked when I created it.
But if I move the recycle bin icon, all bets are off as to where my icons will end up if I rename or create a new one. Sometimes, my change will stick or It might jump one position to the left or all the way over to the first vacant position in the first column. Sometimes, only one icon/file moves, sometimes multiple ones.
This does NOT seem to affect folders, though. My folders seem to never move.
I gave up expecting that my desktop would be 100% stable without 3rd party assistance so DesktopOK is a winner for me. I use its portable version. . I don't mind moving one or two I've added if I restore positions from the last time I saved them, but I'll cuss a blue streak if I have to rearrange them all.