Submit the one-time-login request form at /user/password, which core keys by either a username or an email address in the same name field.
Assumes the form is already on screen — pair it with "Given I am on the password reset page" — so the step stays usable when the form is reached from the login screen's own tab instead.
Examples
When I request a new password for "admin"
And we request a new password for "editor"
When request a password reset for "admin@example.com"
And I request a password reset for "no-such-user"
When we request a new password for "site_manager"
Pattern
When(/^(I |we )*request a (?:new password|password reset) for "([^"]*)?"$/, …)
Part of @webship-js/drupal-core-steps (github.com/webship/drupal-core-steps), a step pack for Webship-js 2.0.x.