If that Jennifer had lived, and you used the name, she, and many others, would be thrilled. If she had died recently, it would be the same. People would compliment you on your choice.
Why does that change because Jennifer was born still? It's still just as lovely a thing to do - and possibly a little more so. See if you can talk to the gran about it, gauge her reaction. It might just make her year to know that someone is going to properly acknowledge her precious little bundle, who would have been born in a time when these things were hidden.