The Palmer Orphanage was located in Columbus, MS. It is listed in a special census of dependent children which was conducted in 1923. As far as I know, the names of the children were not taken, just statistics. The census says that the orphanage was for white children, under the auspices of the Presbyterian Church. It was established in 1898.
A directory from 1978 lists Palmer Home, POB 746, Columbus MS 39701.
The second institution in Columbus was established in 1921: the Masonic Home for Boys. Under the auspices of the Grand Lodge of Mississippi.
The best advice for research would be to check the 1920 census. It was indexed by surname according to the Soundex code, but it might be simpler to just read all the entries in Columbus. A branch library of the Family History Library (in Salt Lake City, UT) could help you do the research.