Welcome captainwilkie. Do you keep your boat near Sheepshead Bay, south shore area?
As for renaming your boat, see here: 48° Vigor's Interdenominational Boat Denaming Ceremony
As to halyard replacement most folks seem to like to go with all rope halyards as the newer high tech lines can be very low stretch. Going with a rope/line halyard is dependent on having a suitable sheave at the top of the mast though. It sounds like the sheave box at the top of your mast could use a re-think or perhaps just new sheaves. See replacement sheaves here: McMaster-Carr
I can't help you with a manual for your Morgan 24/25. Is there a Morgan owners group somewhere out there on the web? That would likely be your best bet for getting a copy of the manual.