The answer to your question is that you don't actually need to disclose the name(s) of the foreign person(s) making the gift in excess of $100,000 (which triggers the requirement to file Form 3520 in the first instance).
However, you certainly can do so if you wish, by entering their name in the description of the gift itself, in Section IV, Item 54(b), on Page 6 of Form 3520. For example, you could report something there like "John Lee, grandfather, gave gift of $$$ in US Dollars."
For more information on Form 3520, a discussion of it, and how to file this with the IRS, please refer the following AnswerXchange post:
https://ttlc.intuit.com/questions/3686254-i-need-to-file-form-3520-this-year-can-i-still-use-turbota...
Speaking strictly of Form 3520 being used to disclose a foreign gift (Form 3520 has other purposes as well), you would want to fill out only the sections indicated by Yellow Highlighter, as found in the screen-capture images attached to the text, directly beneath this answer; simply click the pictures to open. Essentially, you are (mostly) right about what you need to fill out here, as you write in your original question.
Thank you for asking about this important subject.
