Search through rows in entire column

I'm writing a simple Excel VBA program to search through the entire client database, looking for the specific record. While doing this, I've encountered a problem - after encountering first match, it does the instructions well and stops.

The database consists of 500+ rows and looks like this:

Column A Column B Column C Column D

Name xxxx yyy zzzz

Here's some simplified code

Sub Analizuj_1_Click()

Dim SearchName As String
Dim CColumn As Integer
Dim Match As Boolean
Dim CRow As Integer
Dim CRowPaste As Integer

On Error GoTo Err_Execute


LDate = Range("NazwaKlienta").Value
Sheets("2019").Select

'Starting in Column A, Row 2'
LColumn = 1
LRow = 2
LRowPaste = 2

LFound = False
While LFound = False
  'Found a blank cell -> terminate'
  If Len(Cells(CRow, 1)) = 0 Then
     MsgBox "Klient nie ma zaległości"
     Exit Sub
  'Found Match
Szukaj:   ElseIf Cells(CRow, 1) = SearchName Then
     Cells(CRow, 1).EntireRow.Select
     Selection.Copy
     Sheets("test").Select
     Cells(CRowPaste, 1).Select
     Selection.PasteSpecial Paste:=xlValues, Operation:=xlNone, SkipBlanks:= _
     False, Transpose:=False
     LFound = True
     CRowPaste = CRowPaste + 1
     Sheets("2019").Select
     'Continuation"
     ElseIf Cells(CRow, 1).Value > 0 Then
        CRow = CRow + 1
        GoTo Szukaj
     End If

   Wend

   Exit Sub

Err_Execute:
  MsgBox "Blad."

End Sub

Even If I try to continue searching through Start statement, it stops at the first found match. I tried to experiment with other methods and still the same problem.

Inb4 I know, selecting is not the most efficient method for anything