Apart than the altered cell, Conditional Formatting should not be used to change other cells. Please copy the following code event into the discussion code module's sheet:
Option Explicit
Private Sub Worksheet_Change(ByVal Target As Range)
If Target.Count > 1 Then Exit Sub 'it works only for A SINGLE CELL CHANGE
If Not Intersect(Target, Me.Range("A:H")) Is Nothing And Target.Row >= 3 Then
Dim lastR As Long: lastR = Me.Range("K" & Me.Rows.Count).End(xlUp).Row
Dim rngNam As Range: Set rngNam = Range("K2:K" & lastR)
Dim f As Range, prevVal As String
If Target.Value <> "" Then
Set f = rngNam.Find(what:=Target.Value, LookIn:=xlValues, Lookat:=xlWhole)
If Not f Is Nothing Then
Me.Range(Target.Offset(-2), Target.Offset(1)).Interior.ColorIndex = f.Offset(, 1).Interior.ColorIndex
End If
Else
Application.EnableEvents = False
Application.Undo
prevVal = Target.Value
Target.Value = ""
Set f = rngNam.Find(what:=prevVal, LookIn:=xlValues, Lookat:=xlWhole)
If Not f Is Nothing Then
Me.Range(Target.Offset(-2), Target.Offset(1)).Interior.ColorIndex = xlNone
End If
Application.EnableEvents = True
End If
End If
End Sub
When the name is cleared, the interior of the cell is also cleared.
To open the sheet code module window, right-click on the sheet on which you're trying to insert the appropriate names, select View Code, and then paste the aforementioned code into the resulting window.
Of course, you have to have the names given (in the "K:K" column) and the colour of the interior cells that match in the next one ("L:L").