Of course, you could store the city and the full school name, then using the technique we discussed in this forum a couple of weeks ago, remove the city from the school name when required.
I.E.
SELECT school
, city
, TRIM(REPLACE(school, COALESCE(city,''), '')) as short_school
FROM school;
+------------------------------+----------------+----------------------+
| school | city | short_school |
+------------------------------+----------------+----------------------+
| Bloomington North | Bloomington | North |
| Columbus East | Columbus | East |
| Fort Wayne Bishop Dwenger | Fort Wayne | Bishop Dwenger |
| Neil Armstrong High | NULL | Neil Armstrong High |
| Davy Crockett School | San Antonio | Davy Crockett School |
| Kokomo | NULL | Kokomo |
| Logansport | NULL | Logansport |
| Marion | NULL | Marion |
| Jefferson | Lafayette | Jefferson |
| McCutcheon | Lafayette | McCutcheon |
| Harrison | West Lafayette | Harrison |
| Carmel Greyhounds | NULL | Carmel Greyhounds |
| Zionsville Eagles | NULL | Zionsville Eagles |
| Fishers Tigers | NULL | Fishers Tigers |
| Noblesville Millers | NULL | Noblesville Millers |
| Westfield Shamrocks | NULL | Westfield Shamrocks |
| Hamilton Southeastern Royals | Hamilton | Southeastern Royals |
+------------------------------+----------------+----------------------+