Unless your on a PLUS enterprise plan you need to do that before checkout with line-item-properties as a theme customization, or entirely AFTER checkout such as with shopify-forms and metaobjects; though really should use both to bookend the process. Plus plans can use in-checkout checkout extensions.
Here’s a tutorials for VINTAGE themes the code savvy can adapt https://community.shopify.com/t/product-pages-get-customization-information-for-products/7588, https://community.shopify.com/t/cart-use-cart-attributes-to-collect-more-information/7495
If you have an MODERN OS2.0 theme and need such customization , or the process setup/consulted on, you can reach out to me for services.