For a paper that I am writing, I have encountered an issue in which one of my sources has the same last name as myself, of which in in-text citations, makes it appear as if I am citing myself. Do I need to do anything special for such a case? Thank you.
From the MLA Handbook, 8th ed., p. 55:
There are circumstances in which a citation like "(Baron 194)" doesn't provide enough information to lead ambiguously to a specific entry. If you borrow from works by more than one author with the same last name (e.g., Naomi Baron and Sabrina Alcorn Baron), eliminate ambiguity in the citation by adding the authors's first initial (or, if the initial is shared too, the full first name.)
Of course, if you don't cite yourself at all, then there would be no ambiguity if the reader refers to the works-cited list. So, the real question is, do you prevent ambiguity prior to having the reader flip to the end of the work to see that you're not citing yourself?
This isn't directly answered; however, it is addressed indirectly on p. 19:
Minimizing interruptions is a goal in many kinds of writing. If readers are to be engaged and involved in an idea or issue, the reading process should be smooth and unimpeded. Every time readers have to stop and figure something out—whether it's deciphering the intent of stray punctuation, puzzling over a misspelled or misused word, stumbling over a an incorrectly structured citation, or wondering about a reference to a source not in the works-cited list—they are distracted from the argument at hand, and their distraction hinders engagement with the author's point. If a piece of writing is as clear and error-free as possible and if its documentation is trustworthy, readers will remain focused on the idea.
Based on this, if adding the first initial of another author with the same surname as you prevents a reader from interrupting their reading to flip to the back of the work in order to check if the author mentioned is actually you, then that serves the goal of minimizing reader interruption.
In short, even if there is only a single author listed in the works-cited list with your surname, if you think it would cause confusion to not use the initial of their first name in the in-text citation, then I don't think it would be inappropriate to add that initial. (Just make sure that, if you do, you do so for every in-text citation.)
On the other hand, this will depend on context. If you've introduced the other author in the text of your document, and in such a way that it's clear it's not you, then there would likely be no need to add their first initial, since there would be no confusion in the first place.
I agree with Jason that you should also give a first name or initial with the last name to differentiate it from yours (or anyone else mentioned who shares that last name). This advice is geared for times when you cite two or more authors with the same surname, but it works when one of the surnames is the paper author (you).
In addition to this, you can add the phrase "no relation to author" in parentheses when citing the author within the text. Do this for the first mention only. Then continue to cite your namesake in a usual fashion, but continuing with the initial or first name.
In 2018, M. Curie (no relation to author) [plus rest of citation if needed at this point] found that....