What was the first instance for both Superman and Batman of the reader learning the name of their human mother? I am looking for a rough idea of real life time (year) as well as issue number.
From The Origin of Batman it appears the first proper mention of Martha Wayne was in Batman Vol 1 #47 June 1948 Within that site is a link to a Detective Comics Vol 1 #33 1939 which has the annotation of "Dies in flashback Not yet named".
From Jonathan and Martha Kent it appears that the adoptive parents names has changed during the early period of Superman and only becoming consistent/canonized later:
Pa Kent is first named Jonathan in Adventure Comics v1 #149 (Feb 1950). Ma Kent is first named Marthe in Superboy v1 #12 (Jan-Feb 1951) and Martha in subsequent appearances. Her full name is given as Martha Hudson Clark Kent in answer to a letter writer's query in Superman v1 #148 (Oct 1961).
Later stories, after the early 1960s introduction of DC's Multiverse system, declare that the early version of the Kents are named "John and Mary Kent" and live on the world of "Earth-Two", home of the Golden Age DC superheroes, while the more modern Jonathan and Martha Kent live on the world of "Earth-One", home of the Silver Age DC superheroes.
So Batman's mother seems to have the earliest of the commonly known names known to readers. Although "Mary Kent" was introduced in Superman #1 1939.
I add to Morrison Chang's answer the suggestion that possibly Superman's Kryptonian biological mother Lara was named first.
According to Wikipedia:
Lara first appeared in the Superman newspaper comic strip in 1939, where she was first named "Lora." Her first comic book appearance (after being mentioned in the 1942 text novel The Adventures of Superman by George Lowther, where she was named "Lara" for the first time) was in More Fun Comics #101 in January–February 1945. A 1948 retelling of Superman's origin story subsequently delved into detail about Lara, though her more familiar Silver Age aspects became more firmly established starting in the late 1950s and over the course of the next several decades.
So it seems that Superman's biological mother on Krypton was given a name as early as 1939 and had her present name of Lara in comic books as early as More Fun Comics #101 in January–February 1945, about 6 years before his adoptive human mother on Earth was named Martha in Superboy v1 #12 (Jan-Feb 1951), and about 3 years before Batman's mother Martha Wayne was named in Batman Vol 1 #47 June 1948.