I actually thought of this, what if there was a tradition to re-name a state after a President when he died, Soviet style. In cases where a state that could plausibly be called the President's home state could not be renamed, a large city associated with him would be renamed.
You could restrict the tradition to just the state capitols, that would be slightly less insane.
Assuming this doesn't butterfly away the historical administrations:
VA -Washington
MA -Adams
MO -Jefferson (Virginia is taken and the state is associated with the Louisiana purchase, plus IOTL the capitol was named after Jefferson)
WI -Madison (similar logic, Wisconsin was admitted about the time Madison died and the capitol was named after him, otherwise a city in Virginia)
(no state for Monroe but Richmond is renamed after Monroe)
(no state for Adams since the family name is already associated with a state)
TN -Jackson
NY -Van Buren
IN or OH -Harrison (IN would be more convenient since it would cover the grandson as well)
(Tyler gets a small city near where he grew up, maybe Newport News)
KY -Taylor
(Fillmore gets a city in upstate New York)
NH -Pierce
PA -Buchanan
IL -Lincoln
(Andrew Johnson gets a small city in eastern Tennessee)
OH -Grant
(Hayes gets a city in Ohio)
(Garfield gets a city in Ohio, probably Cleveland or Lorain)
(Arthur gets a small city near New York City)
NJ -Cleveland
(McKinley gets a city in Ohio, probably Canton)
(Roosevelt probably gets Oyster Bay or Hempstead in New York)
(Taft gets Cincinnati renamed after him)
(Wilson gets Princeton or Trenton in New Jersey)
(Harding gets another Ohio city)
Coolidge -Vermont
Hoover -Iowa
(probably Hyde Park, NY for FD Roosevelt)
(Kansas City or Independence are renamed for Truman assuming Missouri is taken)
KS -Eisenhower
(Boston is renamed for Kennedy)
TX -Johnson
(given the resignation, Nixon is stuck with a city in southern California)
(Ford probably gets just a city, likely Grand Rapids, Michigan though Nebraska is a possibility)
CA -Reagan
The others are not dead yet, but Arkansas, Georgia, and Hawaii and two cities in Texas would be renamed