Some typesetting styles use small caps on surnames, e.g., "Mᴀᴏ Zedong's Little Red Book". If the surname comes last, however, I'm not sure whether or not the possessive apostrophe-ess should be styled with small caps or without. Here is an example as an image with fonts that make the difference visually clear!
The second version seems typographically better, but the first seems more semantically correct.
There is a related discussion here from a "Graphic Design" point of view: "Small caps in names as part of an adjective". The top-rated answer there says, among other things:
There is no logic to having any word ever be partially small caps.
That advice would apply to contractions, since they are words.
However, if small-caps is considered to bind to names, then "DICK'S" could -- no matter how improbably -- be parsed as a surname that contains an apostrophe.
According to comments on this other question I've referenced, style manuals do not discuss the issue.
Here is a sentence to which the answer could be applied. Note, this person has a two-part surname.
"Since Patricia Law Hatcher’s Producing a Quality Family History was published in 1996, there have been some major changes in the way typography and publishing affect genealogists."