EDIT

The newTaxon wizard does not allow deleting the parent taxon anymore. To create a orphan taxon the user should use the bulk editor.

I got a very similar NPE when deleting the "reuse existing name":

last remote method : http://test.e-taxonomy.eu:80/cdmserver/rem_conf_am/remoting/common.service
last remote request client time : 2021-01-21T10:11:20.431
last remote request response header time : Thu, 21 Jan 2021 10:11:20 GMT
client error time : 2021-01-21T10:11:49.122
login : admin
editor version : 5.19.0.202101202349
server : test.e-taxonomy.eu (edit-test) / rem_conf_am
schema version : 5.18.6.0.20201124
os : Windows Server 2012 R2 6.3 amd64
java : 1.8.0_121
java.lang.NullPointerException
    at eu.etaxonomy.taxeditor.ui.section.classification.TaxonNodeDetailElement.handleEvent(TaxonNodeDetailElement.java:352)
    at eu.etaxonomy.taxeditor.ui.section.AbstractCdmDetailElement.propertyChange(AbstractCdmDetailElement.java:209)
    at eu.etaxonomy.taxeditor.ui.element.AbstractCdmFormElement.firePropertyChangeEvent(AbstractCdmFormElement.java:230)
    at eu.etaxonomy.taxeditor.ui.selection.EntitySelectionElement$DeleteListener.widgetSelected(EntitySelectionElement.java:388)
    at org.eclipse.swt.widgets.TypedListener.handleEvent(TypedListener.java:249)
    at org.eclipse.swt.widgets.EventTable.sendEvent(EventTable.java:84)
    at org.eclipse.swt.widgets.Display.sendEvent(Display.java:4418)
    at org.eclipse.swt.widgets.Widget.sendEvent(Widget.java:1079)
    at org.eclipse.swt.widgets.Display.runDeferredEvents(Display.java:4236)
    at org.eclipse.swt.widgets.Display.readAndDispatch(Display.java:3824)
    at org.eclipse.jface.window.Window.runEventLoop(Window.java:818)
    at org.eclipse.jface.window.Window.open(Window.java:794)
    at eu.etaxonomy.taxeditor.navigation.navigator.e4.handler.NewTaxonNodeHandlerE4.execute(NewTaxonNodeHandlerE4.java:58)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:498)
    at org.eclipse.e4.core.internal.di.MethodRequestor.execute(MethodRequestor.java:55)
    at org.eclipse.e4.core.internal.di.InjectorImpl.invokeUsingClass(InjectorImpl.java:282)
    at org.eclipse.e4.core.internal.di.InjectorImpl.invoke(InjectorImpl.java:264)
    at org.eclipse.e4.core.contexts.ContextInjectionFactory.invoke(ContextInjectionFactory.java:132)
    at org.eclipse.e4.core.commands.internal.HandlerServiceHandler.execute(HandlerServiceHandler.java:152)
    at org.eclipse.core.commands.Command.executeWithChecks(Command.java:494)
    at org.eclipse.core.commands.ParameterizedCommand.executeWithChecks(ParameterizedCommand.java:488)
    at org.eclipse.e4.core.commands.internal.HandlerServiceImpl.executeHandler(HandlerServiceImpl.java:210)
    at org.eclipse.e4.ui.workbench.renderers.swt.HandledContributionItem.executeItem(HandledContributionItem.java:433)
    at org.eclipse.e4.ui.workbench.renderers.swt.AbstractContributionItem.handleWidgetSelection(AbstractContributionItem.java:454)
    at org.eclipse.e4.ui.workbench.renderers.swt.AbstractContributionItem$3.handleEvent(AbstractContributionItem.java:482)
    at org.eclipse.swt.widgets.EventTable.sendEvent(EventTable.java:84)
    at org.eclipse.swt.widgets.Display.sendEvent(Display.java:4418)
    at org.eclipse.swt.widgets.Widget.sendEvent(Widget.java:1079)
    at org.eclipse.swt.widgets.Display.runDeferredEvents(Display.java:4236)
    at org.eclipse.swt.widgets.Display.readAndDispatch(Display.java:3824)
    at org.eclipse.e4.ui.internal.workbench.swt.PartRenderingEngine$4.run(PartRenderingEngine.java:1121)
    at org.eclipse.core.databinding.observable.Realm.runWithDefault(Realm.java:336)
    at org.eclipse.e4.ui.internal.workbench.swt.PartRenderingEngine.run(PartRenderingEngine.java:1022)
    at org.eclipse.e4.ui.internal.workbench.E4Workbench.createAndRunUI(E4Workbench.java:150)
    at org.eclipse.ui.internal.Workbench$5.run(Workbench.java:693)
    at org.eclipse.core.databinding.observable.Realm.runWithDefault(Realm.java:336)
    at org.eclipse.ui.internal.Workbench.createAndRunWorkbench(Workbench.java:610)
    at org.eclipse.ui.PlatformUI.createAndRunWorkbench(PlatformUI.java:148)
    at eu.etaxonomy.taxeditor.Application.start(Application.java:20)
    at org.eclipse.equinox.internal.app.EclipseAppHandle.run(EclipseAppHandle.java:196)
    at org.eclipse.core.runtime.internal.adaptor.EclipseAppLauncher.runApplication(EclipseAppLauncher.java:134)
    at org.eclipse.core.runtime.internal.adaptor.EclipseAppLauncher.start(EclipseAppLauncher.java:104)
    at org.eclipse.core.runtime.adaptor.EclipseStarter.run(EclipseStarter.java:388)
    at org.eclipse.core.runtime.adaptor.EclipseStarter.run(EclipseStarter.java:243)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:498)
    at org.eclipse.equinox.launcher.Main.invokeFramework(Main.java:673)
    at org.eclipse.equinox.launcher.Main.basicRun(Main.java:610)
    at org.eclipse.equinox.launcher.Main.run(Main.java:1519)

When opening the NodeEditor from classification the parent field is still empty. When selecting a parent the Labels are repeated:

These are different issues but very related to the given issue therefore I mention it here. If difficult to fix feel free to move to new ticket for next milestone.

The fix for the original problem is acceptable as adding a taxon without parent is a very rare action.

The NPE when removing reused name is fixed. The problem when removing parent is a little more difficult, therefore the selection of the parent node is disabled and move this ticket to the next release.

splitted the ticket: ticket #9412 handles the exception when reusing a name and this ticket the NPE when removing a parent.