How to get step name on checkout page in magento 2?

You can use the Magento_Checkout/js/view/progress-bar component or Magento_Checkout/js/model/step-navigator componen (used by progress-bar) inside your custom block template/component.

Using progress-bar:

var registry = require('uiRegistry'),
    progressBar = registry.get('index = progressBar'),
    firstStep = progressBar.steps()[0];

progressBar.isProcessed(firstStep); // returns bool, shipping step by default 

Using step-navigator:

var stepnav = require('Magento_Checkout/js/model/step-navigator');
stepnav.getActiveItemIndex() // returns int - 0 for shipping & 1 for payment by default

or:

var registry = require('Magento_Checkout/js/model/step-navigator');
registry.isProcessed('shipping'); // returns bool, you are on shipping step