To provide additional info, then post another message in the same thread as you did now. For any future requests to post you workbook, use a free (and without any sign in procedure) file sharing site and post back the download link.
Back to your query:
Since you said you are very new to macro's it is probably best to create a copy of your workbook. Actions done by macro's cannot be undone by using the blue arrows.
So a non existing sheet name can be entered in column E. I'm sure the other sheets have a specific format. Create a template sheet with that format and call it "Template".
To implement the code below, right-click the sheet "FY18 budget tracking" tab and select View Code. Copy the code in the big white field.
Remember that the code will only run when you confirm an entry in column G.
Here is the code:
Private Sub Worksheet_Change(ByVal Target As Range)
If Intersect(Target, Columns("G")) Is Nothing Then Exit Sub
If Not SheetExists(Target.Offset(0, -2).Value) Then
ActiveSheet.Name = Target.Offset(0, -2).Value
Sheets(Target.Offset(0, -2).Value).Range("A" & Rows.Count).End(xlUp).Offset(1, 0)
Function SheetExists(SheetName As String) As Boolean
SheetExists = False
On Error GoTo NoSuchSheet
If Len(Sheets(SheetName).Name) > 0 Then
SheetExists = True