I am looking for a census record for Louisiana for 1893 to see what the common last names were (research for historical fiction.)

The U.S. Census, taken since 1790, is taken on the "0" year...... 1890, 1900, 1910.   There is no 1893 U.S. census.   As to a state census.... for Louisiana,  They decided in 1898 to use the U.S. Census.  According to one source I have, the only state censuses of 1853 and 1858 have been found.  Instead, you could use name indexes for the 1900 census, leaving blank the names of the person, and asking for any 7 year old born in Louisiana.  FamilySearch.org has that capability (registration required, but it's free).  A less resolution strategy would be to go to a site like findagrave, look for people born in 1893 and buried in Louisiana but they could have been born elsewhere and women if married you won't see their maiden names.  Also, a similar approach using the Social Security Death Index leaving the names blank and asking for people born in 1893 and whose social security number was issued by Louisiana....  but the best approach would be the 1900 census indexes.