The API "searchPerson" action allows you to search the person profiles on WikiTree, much as you would through a web browser at Special:SearchPerson. The parameters include key/search values to match against fields in each person profile, as well as some option that control how broadly or narrowly the search is performed. As with other API functions that retrieve profiles, you can also specify a "fields" parameter to indicate which of the data fields you want returned for each matching profile (See getProfile.md doc page).
Rather than reproduce the form you can see at Special:SearchPerson here, this simple example will do a simple search for profiles of people with your last name.
What is your surname?