This idea has been tried before by many businesses. Allowing your shoppers to name their own price is a creative way to get your business some attention and set it apart from your competitors. These 2 “Pay What You Like” plugins add this feature to your site:
WooCommerce Pay Your Price: allows your visitors to name their own price. You can also use this to accept donations or get a better idea about your pricing strategy.
Shatner: another plugin that allows flexible pricing on WooCommerce sites. This is a free plugin.
There were a few other plugins that we tested but have since been removed from WordPress.org and CodeCanyon. The above plugins get the job done though.