If an author’s name is partly illegible in the source, and you do not know the name, then in your works-cited-list entry you may type out the legible parts of the name and use em dashes to represent the parts that are illegible:
Tu—r, Be—. Letter to Aunt Rose. 17 Apr. 1920. Manuscript.
Your in-text citation should key to the author’s surname as it appears in the entry:
Another writer expressed similar sentiments about the war’s aftermath (Tu—r).
Or you may incorporate the name into your prose:
Another writer, identifiable only as Be— Tu—r, expressed similar sentiments about the war’s aftermath.
If you can determine the name through other means, follow the guidance in section 5.122 of the MLA Handbook, on supplying missing information.
MLA Handbook. 9th ed., Modern Language Association of America, 2021.