If you refer to two people with the same last name, repeat their full names for subsequent mentions whenever your reader might not be certain which person you are discussing. For example, in the following excerpt, from an essay by Melissa Girard that mentions several people with the last name Johnson, the author gives the full name of each person in most instances:*

“Redding makes nearly identical claims about Helene Johnson, the cousin of Dorothy West. . . .”

“Redding hails James Weldon Johnson’s preface to The Book of American Negro Poetry . . . as an important ‘scholarly essay.’”

But when the reference is clear, Girard uses only the last name:

“Redding hails James Weldon Johnson’s preface to The Book of American Negro Poetry . . . as an important ‘scholarly essay.’ Redding’s endorsement highlights a growing institutional divide: Johnson’s poetics will be part of the new academy, while the so-called ‘school teachers’ will become minor. Redding’s comments are clearly meant as a sign of respect for Johnson, but they are, strictly speaking, untrue.”

Even though Helene Johnson was mentioned earlier in the essay, once the focus is on James Weldon Johnson, Girard does not need to repeat “James Weldon.” 

Note, however, that although first names are spelled out when you need to specify whom you are referring to in your writing, when works by authors with the same last name are given in the works-cited list, parenthetical references to those works should only give the first initial and last name of the author: 

Grimké, for instance, had seen her poetry published in almost all the major anthologies of New Negro Renaissance poetry, including . . . Ebony and Topaz (C. Johnson). . . .”

Works Cited

Johnson, Barbara. The Feminist Difference: Literature, Psychoanalysis, Race, and Gender. Harvard UP, 1998.
Johnson, Charles S., editor. Ebony and Topaz: A Collectanea. 1927. Books for Libraries Press, 1971.
Johnson, James Weldon, editor. The Book of American Negro Poetry. Harcourt, Brace, 1922.

*Examples are taken from Melissa Girard; “J. Saunders Redding and the ‘Surrender’ of African American Women’s Poetry”; PMLA, vol. 132, no. 2 (2017), pp. 281-97.