A school friend's little sister is
Lindsey, but she's always called
Lindy.
Lindy's best friend is, and is called,
Lindsey. So I grew up with a vague sense of confusion!
Lindsay for a boy,
Lindsey for a girl. Not that I've met more than one male
Lindsay ... and that was before it becam popular for girls.
Not sure about a linden connection.
Love the tree, though, and the sound of the name
Linden. I also find
Linda genuinely pretty in spite of being dated to the 1940s-1950s. But realistically I don't think I'd use any of them: there are too many names I like more.