I'm am Alexandra and have never changed it to Alexa. In fact I HATE my name.
Why? Because although Alexandra is nice, Alex is very unisex and mostly associated with boys. When I was at school, people used to ask me why I had a boys name and eople think I'm male until they meet me. I often get addressed as Alexander- the make form.
I think Alexa is an even worse version of Alex. Alexandra doesn't go with my marriage Irish surname either, so I am thinking of changing my name from Alexandra to something more feminine.