This robot is named "the last man" by the artist, Mel Hunter, as noted in the December 1959 issue:
Mel Hunter's cover this month is the third in his series for F&SF concerning the adventures of "the last man." The first, you may remember, showed him tenderly watering a rose richly blooming in a desert wasteland; in the second, he was wistfully poring through mail order catalogues he had unearthed in an old packing crate. As for his discovery of the new Eve in his current adventure — Mr. Hunter is resolutely uncommunicative as to when, or even if, a marriage will take place. Follow F&SF's covers faithfully so that you will be sure not to miss the next disturbing installment. . . .
There are few other notes about the cover art, other than the May 1960 cover being titled "Music to Watch the Moon Rise By" and an announcement in January 1970 of the upcoming series of covers:
THIS MONTH'S COVER is the first of a series of six new robot paintings done for F&SF by Mel Hunter. The remaining five will be published during the next two years. You can begin a collection of this superb robot series by ordering this month's cover with the coupon above.
Mel Hunter's "The Last Man" covers appeared on the following issues of F&SF:
There is a special note about the May 1970 cover but it doesn't really give us any more information about the subject:
ABOUT THE COVER
It is not clear whether the robot's post-holocaust collection of F&SF is complete, but he appears to have enough good reading for some time (e.g., in the foreground is the March 1958 issue, with stories by Shirley Jackson, Robert Bloch and Poul Anderson, among others).
This latest of Mel Hunter's robot series is a preview of a cover that was done specially for a new anthology which celebrates F&SF's 20th anniversary. The book, TWENTY YEARS OF FANTASY AND SCIENCE FICTION, will be published late this Spring by G. P. Putnam's.
The Encyclopedia of Science Fiction notes that there were 16 works in the series, which was concluded with a specially commissioned cover in 2003, shortly before his death in 2004.