If you want to add text to the end of the file use this instead, For Output overwrites/creates files, Input reads files and Append adds to files
code:
Private Sub Command1_Click()
Dim namefile As String
namefile = Text1.Text
Open App.Path & "\Accounts\" + namefile + ".txt" For Append As #1
Print #1, Text1.Text
Print #1, Text2.Text
Print #1, Text3.Text
Print #1, Text4.Text
Close #1
MsgBox "Msgbox"
End Sub