I have no connection to this family.Saw your query anddid some searching.This is what I have found:
1910 United States Federal Census about Elmer Eakins Jr. Name: Elmer Eakins Jr. Age in 1910: 25 Estimated birth year: abt 1885 Birthplace: Pennsylvania Relation to Head of House: Nephew Father's Birth Place: Pennsylvania Mother's Birth Place: Pennsylvania Home in 1910: Philadelphia Ward 32, Philadelphia, Pennsylvania Marital Status: Single Race: White Gender: Male
Household Members: Name Age Sarah Eakins 67, head, single, b. Penna, own income Clara Eakins 51, sister, single, b. Penna., own income Elmer Eakins 49, brother, single>, b. Penna, proprietor, Dr? House Elmer Eakins Jr. 25, nephew, b. Penna, chemist, steel works Fannie Holmes 58, boarder
NameRelation Marital Status Gender Race Age Birthplace Occupation Father's Birthplace Mother's Birthplace James EAKINSSelfMMaleW65PAMoulderIREIRE Ellen EAKINSWifeMFemaleW59PAPAPA Emma EAKINSDauSFemaleW36PAAt HomePAPA Sarah A. EAKINSDauSFemaleW34PA... StorePAPA Mary J. EAKINSDauSFemaleW32PAAt HomePAPA John EAKINSSonSMaleW30PAPainterPAPA Claira EAKINDauSFemaleW21PAAt HomePAPA Elmer E. EAKINSSonSMaleW18PAPrintingPAPA
Source Information: Census Place Philadelphia, Philadelphia, Pennsylvania Family History Library Film1255179 NA Film NumberT9-1179 Page Number385D ********************************
With that information you probably can send for Elmer's birth certificate to get his parents' names.
Regards, Susan Nass Random Acts of Genealogical Kindness