The name Eveline means "little, or small, Eve" which is Hebrew for "life." Of course, the connotations associated with the name Eve are those of the first woman who tempted her mate Adam with the apple from the serpert, an act which expelled them from the Garden of Eden.
On the other hand, the meaning of "life" and the diminutive suffix of -lyn, or -line suggest that Eveline lives a small life, which certainly seems to be her situation as she sits in the darkening window, feeling "tired." In fact, the concept of paralysis drives the narrative of "Eveline." For, as Eveline leans her head against the curtains of "dusty cretonne," she dwells on her life, limited by the violence of her father, her obligations to her brothers, and the demeaning treatment of Miss Gavan. Indeed, she seems prohibited from attaining happiness and respect, trapped in a stultifying life of obligations.
It was hard work--a hard life--but now that she was about to leave it she did not find it a wholly undesirable life.
Eveline's paralysis leads her to find some sense of security in her stifling life because she fears the unknown. Thus, when "[A] bell clanged upon her heart, and her sailor Frank seizes her hand, Eveline fears the future--"he would drown her"--and she refuses to move. She forsakes escape, life and love, instead choosing the past, her obligations, and death-in-life, not unlike the first Eve who lost much after her fateful decision in the Garden of Eden.