Per my mother, my maternal great grandmothe’s name was Liba Yaruchamovitch. She lived in Vitebsk and that is where my grandmother, Anna Rachel Yaruchamovitch was born. The death certificate of my grandmother per Ancestry records, (DOD: 12/30/36) lists her mother and father’s names as Liba Kusherman and Jacob Erikoss. My grandmother is buried in Washington Cemetery in Brooklyn, NY.

Any suggestions as to identify which are the “real” names?

Thank you.
--
Alice Simon Berger

It is possible they both are.
In Russia it was and still common for woman to be known by their father's first name with a suffix "vitch" added to it.
Liba Kusherman's father 's first name might have been Yerucham so she was known as Liba Yeruchamovitch, but her family last name was Kusherman.
Yerucham is a biblical name, (see the book of the Prophet Samuel (Shmuel) I 1:1) Yerocham was Samuel's grandfather.

Alice,

Anna DUBROW'S 1911 passenger manifest gives her father's name as Jankel JERUCHINOWICZ.  Which lends credence to your family story of the surname being Yaruchamovitch.

Anna's death cert gives her father's surname as Erikoss.  If you think about someone with an accent trying to tell an American the name JERUCHINOWICZ,  it could sound like ERUKOWICZ, and get transcribed as ERIKOSS.

Benjamin DUBROW arrived in NY in 1910 as Itzig Ber DUBROWNI, age 21, shoemaker, from Witebsk. 
Nearest relative left behind is his wife Henie DUBROWNI in Witebsk. 
Itzig Ber was bound for his brother M. DOBROWNI in Brooklyn.

Benjamin's wife arrived in 1911 as Eine Ruchel DUBROVIN, age 23, from Witebsk.
Nearest relative left behind is her father Jankel JERUCHINOWICZ. 
Jankel's town name is hard to ready (definitely does not say Witebsk.)  Something like Raperansa??
Eine Ruchel is bound for husband Bear DUBROWIN on DeKalb Ave. in Brooklyn.

Also, Anna's death cert gives her cause of death as Pemphigus, which Dr. Google explains as:
"a group of autoimmune skin conditions that cause sores, blisters or fluid-filled bumps to form on your skin."

Johns Hopkins notes that: "Certain ethnic groups are more prone to this condition. This includes people of eastern European Jewish and Mediterranean descent."
https://www.hopkinsmedicine.org/health/conditions-and-diseases/pemphigus-vulgaris

The info on Anna's death cert indicates that she was in Kings County Hospital for nine months.

You can see her death cert through this site:
https://a860-historicalvitalrecords.nyc.gov/search
Because Anna passed on at the end of December 1936, her death cert is filed in 1937.  Brooklyn cert # 43.