If you want to change a piece's name: Deprecate the old piece (add "DEPRECATED" on its own line to the NXMT or NXMO file), and create a duplicate under the new name (don't have "DEPRECATED" on the new one). Please then specifically point this out to Nessy when you submit the update to your styles where this happens; and we'll remove the original version (and get NeoLemmix to redirect to the new one automatically) in a future update.
If you want to remove a piece: Deprecate it instead. Only remove it if it's broken and can't be repaired, and thus "missing piece" errors are a nicer result than whatever happens if the piece remains existing in some form. If it's functional but you just don't want it in the style anymore (eg. perhaps you've replaced an object made up of three seperate pieces, with a resizable nine-sliced single object), then just deprecate it.
In the future (EDIT: V12.8.0 will provide this functionality), I'll likely look into a means where styles can specify the redirects themself, but currently, redirects are specified in a single central file.
And finally - this applies specifically to styles you've released. You can rename / delete as much as you like in unreleased WIP styles.
For the record - deprecating a piece means it still exists and will be found by NeoLemmix, but the editor won't display it in the piece selection list (unless the user specifically chooses to show deprecated pieces). It was specifically implemented for this kind of situation.
