Is it rude to not ask for someone’s name when they ask for yours in middle of a conversation

I’m a bit socially awkward and have become a loner for most of my adult years. Today, I was walking my dog when my neighbour approached me, and we started talking about her newly adopted dog. I was asking her questions, so the conversation wasn’t one-sided. My body language and expression were pretty open. She asked for my name, but I forgot to ask for hers. As we were saying our goodbyes, she told me her name, and that’s when I realized I had forgotten to ask when she asked for mine. I then spent my entire walk thinking about how I lack social skills