New London is not listed in the directory I published in 1982 : "Adoption Agencies, Orphanages and Maternity Homes : An Historical Directory." The coverage of the Directory was mostly for 1923 and later, to serve living adoptees.
There is a set of annual volumes containing all sorts of directory information, but I really don't know if it lists institutions which were under private (nongovernmental) auspices : "The Wisconsin Blue Book." Madison, WI, 1853-1968.
The front pages from annual city directories would list orphanages. A library having a collection of city directories might catalog it at the subject entry "NEW LONDON---DIRECTORIES." The actual titles might have changed every few years. I was unable to find this topic on the online catalog of the Library of Congress, but the online portion may omit thousands of old books.
The federal censuses of 1910 and 1920 can be consulted online to see if there was an orphanage in New London---a city on the border line of Waupaca and Outagamie counties, 27 miles NNW of Oshkosh. Ancestry.com has a search window at the bottom of each page. If you type the name of one of those counties, you might find a message board for that county. If so, read the queries and responses to see if there is a volunteer with census research experience. I have no such experience, but I read the boards for counties in New York State, and people are frequently having trouble finding the proper Enumeration District for censuses.