Most of the time (and all of the time with gendered pronouns), you don't use it to address me. You're using it to talk about me. And then, it's really between you two what you call me, isn't it? Of course I would be happier knowing you didn't refer to me in a rude manner, or as something I'm not, but I believe in privacy too, so it's really your business.
Turkey isn't rude, and it's usually understood from context that we don't refer to the bird (the Turkish government also push Türkiye on countries where the native word has no bird connotation). We used to translate all names, and that's understandable because names are often unpronounceable or otherwise violate grammatical rules if you just blindly drop them in a different language. I think it should be fine to use "Turkey" when talking to another English-speaker.
Turkey isn't rude, and it's usually understood from context that we don't refer to the bird (the Turkish government also push Türkiye on countries where the native word has no bird connotation). We used to translate all names, and that's understandable because names are often unpronounceable or otherwise violate grammatical rules if you just blindly drop them in a different language. I think it should be fine to use "Turkey" when talking to another English-speaker.