Titles of chapters should reflect significant events that take place in the given chapter and also grab the reader's attention. I would consider titling Chapter 1 "The Dead Mouse" because George argues with Lennie about keeping the dead mouse. Lennie's obsession with the dead mouse is significant because it portrays his mental handicap and loving heart. It also depicts Lennie's strength and accident-prone personality. I would title Chapter 2 "Newcomers" because George and Lennie arrive at the bunkhouse and meet their boss.
An enticing title for Chapter 3 could be "The Sound of Death." This title reflects how Steinbeck pays particular attention to the ominous silence surrounding the death of Candy's dog. I would consider titling Chapter 4 "The American Dream" to reflect Lennie's description of the ideal life on a farm with George. Crooks is even enticed by the possibility of living with the two men.
In Chapter 5, Lennie accidentally kills Curley's wife. I would consider the title "Another Bad Thing" because that is what Lennie whispers to himself after realizing Curley's wife is dead. I would title Chapter 6 "Lesser of Two Evils" because George is forced to kill Lennie. Either way, Lennie was going to die. George essentially saved Lennie from a worse experience by killing Lennie before the lynch mob captured him.
Steinbeck takes his title from a poem called "To a Mouse" by Robert Burns. In the poem, a farmer addresses a mouse whose home he has destroyed with the plow. The mouse had made good plans for the winter. He (mouse) had constructed a home made of leaves and "stubble" (sticks and branches) but the plow destroyed it. The title of Steinbeck's novel comes from the lines "The best laid schemes of mice and men, / Go often askew." In other words, even our best plans can be destroyed. George's and Lennie's plans of having a farm "go askew."
So, one way to think about a new title is to take something else from this poem. The penultimate line (next to last line) is "And forward, though I cannot see." This captures the idea that we move into the future, not knowing what will happen.
You might also look/think elsewhere for an alternative title. Consider different aspects of the story. Lennie is obsessed with the rabbits. Something simple like "The Rabbits" is thoughtful but doesn't give any of the story away. "Tending the Rabbits" is also simple but telling once you have read the story. There can be a lot of meaning in simplicity. "The Dream" might be a good title because it refers to their dream of having their own farm. "Chasing the Rabbit" suggests someone chasing something that is difficult to catch. Lennie and George chase a dream but never get it. Even when Lennie gets a hold of a rabbit or a mouse, he inadvertently destroys it. This title illustrates how, even if the rabbit/dream is caught, it is destroyed.