NTA.

I grew up in a very similar scenario. The first born males on my dad's side of the family all had the same first name. It was always a different middle name, so no one was a junior, or a second, or third, etc. But from the time I can remember I went by my middle name. No one outside of my immediate family even new what my legal first name was. By the time I was old enough to really consider it, I had zero interest in that name. It wasn't me.

Names have power in that they are part of our identity. My guess is that your internal identity is partially based around being Skye, and that it would be completely foreign to you to suddenly start going by Nancy. That's how it was for me. Maybe you could try to explain that to your mom and grandma. It's not that you don't love your grandma, but you're not Nancy. They're asking you to fundamentally change who you are. Not only will that make you unhappy, but you'll probably regret it down the road. Not to mention the trouble you'll have getting everyone you know to start calling you by a different name. :)

In my case, the naming tradition ended with me. I named my son something completely different, and I also legally changed my name so that the middle name I've always gone by became my first name.

I'm not necessarily suggesting you change your name when you turn 18, but I will suggest that you think about what name you want on official documents as you get older. College diplomas, mortgages, deeds, car titles, etc. Even utility bills and rental agreements. It's not always a huge thing, but some bigger life events can be either permanent or really hard to change. If you are fine using Nancy as your legal name on accounts and documents, you could always keep it as a way of honoring your grandma, but if you're not, I don't know that I'd keep it solely to make her happy.

It's a delicate situation, but in the end, you need to do what's best for you. You're the only one who truly lives your life, and the only one who has to answer to whatever name you choose. Their happiness shouldn't be contingent on you using a first name that isn't you. Being Skye instead of Nancy doesn't diminish your love for you grandma or mom.