Simlar works, done in 1960 are referred to as “Spectres".  And Robert Miller, in his exhibition in 1996, references them as "Dream Portraits”. I think they may all be part of a larger process she was working through.

The below is paraphrased from Julia Bryan Wilson, "Painting the Self,” in Eva Hesse, San Francisco Museum of Modern Art, February 2 - May 19, 2002, traveling to Weisbaden Museum, Germany, June 15 - October 13, 2002.

I think it describes the journey Hesse was on at this time...

"Fresh out of Yale in 1952 Hesse was concerned that painting was the only viable path to artistic success and she struggled to find her painterly voice.  Despite the positive reception of her drawings Hesse turned her attention to painting and focused her energies on harnessing oil and canvas.  Most of these paintings are untitled.  A few, however have been identified as self portraits.  But if they are all images of self-regard, they are duplicitous for their murky colors yield no clear insights about the artist aside from a sense that she is seriously grappling with process and paint.  These are important, if anxious, works in which Hesse’s major conceptual concerns—questions of materials and the body—are made to matter quite intensely.  In addition to her coming to terms with paint, a medium she would very soon renounce, these works show Hess’s attempts to confront figuration per se.  Looking toward de Kooning’s women, perhaps, Hesse depicted herself as a series of expressive brushstrokes."

These works were the subject of an important exhibition at the Hammer in 2011.  

Here is a link to that exhibition which discusses the series.

https://hammer.ucla.edu/exhibitions/2010/eva-hesse-spectres-1960

This painting dates from 1961, so perhaps not technically part of this 1960 series…but the visual connection is there and the ideas and concepts worked out here are very much the same.

Similar works to the one being offered are in the following collections:



Untitled, 1960

Oil on canvas

18 x 15 inches

The Museum of Modern Art, New York



Untitled, 1960

Oil on canvas

36 x 36 inches

Mugrabi Collection, New York



Untitled, 1960

Oil on canvas

16 1/4 x 16 inches

The Museum of Modern Art, New York

Untitled, 1961

Oil on canvas

16 x 16 inches

The Lewitt Collection, Wadsworth Atheneum, Hartford, CT

There is also a work from this series in the Rachovsky Collection, Dallas.

Also, Ursula Hauser, the Swiss collector and mother of Hauser & Wirth’s Manuela Hauser…, owns three works from this series personally.