How to get component name from general tab of component properties?

Yes, they show up as expected in the component name column and the top level assembly is the display part. Here is the code I was using for this operation:

Option Strict Off
Imports System
Imports NXOpen
Imports NXOpen.Assemblies
Imports NXOpen.UF

Module Names
Public theSession As Session = Session.GetSession()
Public theUFSession As UFSession = UFSession.GetUFSession()
Public Lw As ListingWindow = theSession.ListingWindow

Sub Main()
Lw.Open()
Lw.writeline("First Process")
For Each comp As Component In theSession.Parts.Work.ComponentAssembly.RootComponent.GetChildren
Dim partName As String = ""
Dim refsetName As String = ""
Dim instanceName As String = ""
Dim origin(2) As Double
Dim csysMatrix(8) As Double
Dim transform(3, 3) As Double
theUFSession.Assem.AskComponentData(comp.Tag, partName, refsetName, instanceName, origin, csysMatrix, transform)

Dim partNumber As String = ""
partNumber = instanceName & "Rev1"
Dim thisInstance As NXOpen.Tag = theUFSession.Assem.AskInstOfPartOcc(comp.Tag)

Lw.WriteLine("PartName: " & partName)
Lw.WriteLine("RefsetName: " & refsetName)
Lw.WriteLine("InstanceName: " & instanceName)

' this changes what shows up in Component Properties->General->Name
theUFSession.Obj.SetName(comp.Tag, partNumber)

' uncomment the following line to change the instance name
theUFSession.Assem.RenameInstance(thisInstance, partNumber)
Next

Lw.writeline("Second Process")
For Each Obj As DisplayableObject In theSession.Parts.Display.Views.WorkView.AskVisibleObjects
Dim comp As Component = Obj.OwningComponent

'ChangeWorkPart(Obj.OwningComponent)
Dim partName As String = ""
Dim refsetName As String = ""
Dim instanceName As String = ""
Dim origin(2) As Double
Dim csysMatrix(8) As Double
Dim transform(3, 3) As Double
theUFSession.Assem.AskComponentData(comp.Tag, partName, refsetName, instanceName, origin, csysMatrix, transform)

Dim partNumber As String = ""
partNumber = instanceName & "Modified"
Dim thisInstance As NXOpen.Tag = theUFSession.Assem.AskInstOfPartOcc(comp.Tag)

'Debug - output new name
Lw.WriteLine("PartName: " & partName)
Lw.WriteLine("RefsetName: " & refsetName)
Lw.WriteLine("InstanceName: " & instanceName)

' this changes what shows up in Component Properties->General->Name
theUFSession.Obj.SetName(comp.Tag, partNumber)

' uncomment the following line to change the instance name
theUFSession.Assem.RenameInstance(thisInstance, partNumber)
Next
End Sub
End Module

The first process does not read the name from the component that I would expect, but the second process does. I attempted using the prototype, owningPart, and owningComponent(and combinations of each) with the .Name, .Lead, .DisplayName, and any other properties I thought might be helpful but it appears it is not a proper method for referencing the work component in an assembly.

Most assemblies we use are multi-levels, but for testing purposes, I had an assembly file with 1 parent and multiple children for this code. Do you know how I might be able to reference the work component properly?