From the 1850 United States Census,it looks like Theodore Alden's father and older brother were both named Joseph.
name: Theodore Alden residence: Louisville, part of, Jefferson, Kentucky age: 15 years calculated birth year: 1835 birthplace: Massachusetts gender: Male race (original): race (expanded): death month: death year: film number: 442974 digital gs number: 4192496 image number: 00332 line number: 9 dwelling house number: 307 family number: 363 marital status: free or slave: Household Gender Age Joseph Alden M 49y Adda Alden F 44y Ellen Alden F 20y Joseph Alden M 17y Theodore Alden M 15y James B Slaughter M 35y James Slaughter M 12y Margaret Slaughter F 10y Mary Slaughter F 7y Fanny Slaughter F 2y Teresa Schmenn F 20y
The estimated year of Joseph Alden's birth in the marriage record in 1871. groom's name: Joseph Alden groom's birth date: 1871 groom's birthplace: U S groom's age: 24 bride's name: Bell Tilton bride's birth date: 1876 bride's birthplace: U S bride's age: 19 marriage date: 24 Jul 1895 marriage place: Glendola, Monmouth, New Jersey
The 1900 United States Census has the family prior to Ella's birth. Jas is likely Joseph.
name: Jas L Alden titles & terms: residence: Neptune Township, Monmouth, New Jersey birth date: May 1896 birthplace: New Jersey relationship to head of household: Son spouse: spouse's titles & terms: spouse's birthplace: father: Jas Alden father's titles & terms: father's birthplace: Arkansas mother: Belle Alden mother's titles & terms: mother's birthplace: New Jersey race or color (expanded): White head-of-household name: Jas Alden gender: Male marital status: Single years married: estimated marriage year: mother how many children: number living children: immigration year: enumeration district: 0139 page: 21 sheet letter: B family number: 521 reference number: 86 film number: 1240987 image number: 00179 Household Gender Age parent Jas Alden M parent Belle Alden F Jas L Alden M Chas Alden M Pricilla B Alden F
Charles is missing from 1910 Census
name: Joseph Alden birthplace: New Jersey relationship to head of household: Son residence: Jersey City Ward 8, Hudson, New Jersey marital status: Single race : White gender: Male immigration year: father's birthplace: Arkansas mother's birthplace: New Jersey family number: 361 page number: 17 Household Gender Age parent Joseph Alden M 38y parent Bell Alden F 34y Joseph Alden M 14y Priscilla Alden F 10y Ella Alden F 8y