TagWriter is capable of doing this just fine. I’ve written a basic contact card to my tag with just my name and nothing else. It creates a vcard with N and FN fields, and the format is correct.
The problem might be with the way the data is being stored, but more likely it’s the opening process. Let’s start with some screenshots from taginfo that show how you’ve stored the data, then we can move on from there. Redact any data you don’t want to share.