A couple of times, I’ve read a book or work in progress where a character’s name just doesn’t seem to make much sense in regards to names given to the minor characters. The main might be called something like Aurea or Felicity Von Hubris and then everybody else is John, Sarah and Jo.
There’s nothing wrong with having interesting, unique names for your characters. But try to at least consider the world you’re writing and the time period before you start naming them. There is a reason why you probably know more than one Liam and Sophie at school or in the work place. Equally, someone in a different country will have their own popular names that appear more than once on the class register. This will change for as long as time goes on. Names go in and out of fashion like clothes and music.
The main example here are those who give their non-Japanese characters Japanese names. Of course, if your character has some connection to the nationality behind the name you’ve given them, then there’s no reason why you can’t do that. It’s just you have to be able to present your choices as credible concepts.
As for a character who renames his/herself, wanting a fancy or unusual name can be classed as a reason, but it will usually extend to something greater. i.e. ‘I want to annoy my parents’, or ‘It might make me more interesting to the opposite sex’.
Think about it: when we name our children, and even when we name our pets, we put some thought into what we’re going to call them for the rest of their lives. Your characters are to be treated no differently. Once a name sticks, it can be really hard to change it to something else!