Disappointed1, I really think that you are not being unreasonable. Of course, no-one 'owns' a name. However, that does not make it any less painful for you.
I can relate, in a way. After each of my miscarriages, DP and I have chosen names for our babies. My pregnancies all ended so early that we never had an opportunity to discover the sex. We just decided what sex we felt that the baby would be and chose a name accordingly. After our second MC, DP's DSis picked the same name as we had chosen for our last baby. Her son was born several months after our MC, and we had never told her the name, but yes, it still hurt. Irrational? Yes, but there is no way to control these feelings.
Similarly, after our last MC (a year ago), DP's brother and his partner announced their pregnancy. Exactly two weeks to the day we had had our last MC, in fact. So, when their baby was born, not too long after ours would have been born, it was torture. They insisted we visit them in the hospital the day their baby was born, were adamant that we each hold her, so on. Now, at the time I was hugely upset and also very angry. With hindsight, I now realise that they weren't trying to hurt us. They weren't thinking of us at all, they were just so excited to have a new baby, and so wrapped up in their happy new family bubble. And they were right to be that way. Who wouldn't, after having their first child? I'm hopeful DP and I will have that experience, some day.
I'm sorry, I have written a lot of my experiences. I didn't mean to make this all about me, I just hope, OP, that sharing my story will be of some small help to you. Essentially, OP, you are not being unreasonable, at all. You can't be expected to be reasonable right now. Or even rational. But, like me, you will manage to move past the pain, love the new addition to the family, and become a great Aunt. And hopefully some day, you and your DH will have a baby of your own, and this name won't matter so much, you will be choosing new names and, even better, preparing for a whole new life. Best of luck with TTC. X