A surname note is a way to indicate that while the transcription may accurately reflect what the enumerator wrote the surname recorded is so different from the "correct" surname that users are unlikely to find the record using the normal surname variation options during a search.
Once a surname note is added to a census record a note appears on the search page whenever a person searches for the specified "correct" name:
|There arewith suggested surname of Smith.|
An example of the appropriate use of a surname note is where the enumerator recorded the name Arsenault as Harseno. Someone searching for the name Arsenault is likely aware of several possible spelling variations of that name, but may well not think to check for a spelling beginning with H.
An example of an inappropriate use of a surname note is where the enumerator recorded the name as Mitten, when the usual spelling is Mitton. Minor spelling variations like this are easily handled using the surname variation options on the search page, and to enter a surname note for every name that isn't spelled according to a user's expectation would create so many notes that they would just obscure the cases where they are really needed.
A second appropriate use of surname notes is when a family with multiple generations that include family members with different surnames are recorded using ditto marks such that members end up with the wrong surname. For example if a married daughter and her husband are listed in the middle of a household, and have a different surname, other children of the head of household listed below them are sometimes listed with a ditto mark under the surname even though they are siblings of the married daughter and share the surname of the head of household not the married name of the daughter they appear under. Unless it can be proven beyond reasonable doubt that this is the case these names have to be recorded with the ditto mark interpreted as the surname on the previous line, with a surname note. This way the record can be found using either name.