you can add only one title per product if you want to change title base on variants changes then you have to make custom code to handle it.
like add variants title in variants barcode or SKU field that you are not using and then show it on front end on variants changes.
if you want to change title base on variant change then you have to manage it by SKU or barcode field because we have no direct field to do that.
I tried using other custom fields as product titles but it didn't work for some attributions. I did find a much cleaner way by adding a special character at the end of the product title and before any extra keywords (admin related) so that only the first section of the title will now display on the storefront.
So for instance: "Product Name Keyword1 Keyword2 etc." becomes "Product Name - Keyword1 Keyword2 etc."
See more here...
Then only way to really do this is to use metafields. Create a metafield for your variants, and enter the custom title for each variant into the metafield. Then display the metafield on your product pages/dropdowns. You can easily bulk edit your Shopify store's metafields from Mixtable's Excel-like spreadsheet interface. Map all the metafields you want to columns, update the relevant cells, and sync the data back to Shopify