Do your eyes only scroll to the "name you're really looking for" on a census page? Do you not really think about the names of the neighbors? It's always a good idea to read the page your relative is on and at least a few pages before and a few pages afterwards-in case there are relatives nearby.
A relative married his second wife in the early 1860s. I didn't know much about her--until I reviewed her 1910 census entry when she had moved with her second husband to another state. There, next door, were two widowed brothers with a last name that was her maiden name.
Research is in progress, but if they are not related to her it is a huge coincidence!