In other words it is the belief that's dysfunctional, not the body itself. I have sympathy for those who believe stuff like this about themselves (know they should have been born a man/woman/dog/whatever) because there's clearly something wrong with them.
I identify sometimes as someone I've seen in a film, or a book - I can almost imagine I'm taking on a part of their identity, their facial expressions, the way they speak perhaps. It doesn't last long. It's called escapism. Sometimes 'acting' in this role helps me deal with certain situations better - when I'm finding my children hard work, I sometimes imagine I'm my sister, who is good with children, and I talk a bit like she would or I think 'what would she do?' and it helps me to think from a different perspective.
Stuff like that, I think, is normal - it's a mixture of learning and copying - trying things out. And escaping briefly from the rut you have got into as yourself.
If you then go on to decide that this is your true personality, that you actually are this other person, that would cross the line into deluded. Using other people's behaviour and style and whatever as inspiration, to help build your own self, is normal. It doesn't however change what and who you were born as, in any way.