Turn the one with the less correct name into a redirect. If there is any chance someone will be searching by the alternative name, might as well let them find it. Also reduces the chances for someone adding that wiki again as another duplicate.
Place #REDIRECT [[More Correct Name]] at the beginning of the "Less Correct Name" page (and delete its' contents).
Check source page for useful contents and move it to the destination page.
And leave a note on the talk page of the "More Correct Name" article indicating the redirect, to help maintain any edit history from the "Less Correct Name".