Here's something more compact:

Sub SheetRename()
Dim aPart As String, ePart As String, shtName As String

Range("A1").EntireColumn.Cells(Rows.Count, 1).Select
Selection.End(xlUp).Select
aPart = Selection
ePart = Selection.Offset(0, 4)
shtName = aPart & " " & Format(ePart, "m-d-yy h-mmAM/PM")
ActiveSheet.Name = shtName

End Sub

If compact is your goal, what about this for the body of your SheetRename
subroutine?

Dim R As Range
Set R = ActiveSheet.Cells(Rows.Count, 1).End(xlUp)
R.Parent.Name = R.Value & Format(R.Offset(0, 4).Value, " m-d-yy h-mmAM/PM")

By the way, I used R.Parent.Name to keep the last statement from
word-wrapping in newsreaders... it should be replaced by ActiveSheet.Name
for clarity.

Rick