This is a pretty common scenario. Of course, the core wp imported plugin will work with this. But it will create new entries regardless of which once you already have. You might have imported content before and noticed that there are duplicate posts, this is something I think you can't avoid with the default importer.
Now to help you with this, there are other solutions. WP import all is one of my favourites. The reason, it lets you map the entries from your CSV to WP. You decide entries from which column go to which field.
Here is a free version of the plugin: https://wordpress.org/plugins/woocommerce-xml-csv-product-import/
This does not work with WooCommerce though, you will need a premium plugin for this: http://www.wpallimport.com/woocommerce-product-import/
Another product I can think of is the one built by the WooCommerce folks itself:
https://docs.woocommerce.com/documentation/plugins/woocommerce/woocommerce-extensions/product-csv-import-suite/
I have not used this myself, but have heard good words about it.
PS: If the data from the previous posts is also there on the CSV, you can delete the previous posts and import them from the CSV, that way you won't have to worry about the duplicated, or the check the names. You can try this on a local install. and then export them with all the updated data, and import it again to the production site.
I hope you find this helpful.