I think airport names should reflect the main town or city they serve.
I will take the thread starter's comment that Bristol might be renamed IK Brunel Airport. How many people would know where that was? There is already a Brunel University which is located a hundred miles from Bristol. I wonder how many know where it is situated without looking it up on the Internet.
Locally, Bristol Airport is still referred to by many simply as Lulsgate or Lulsgate Airport (from the nearby charmingly named hamlet, if it even merits that description, of Lulsgate Bottom), whereas, officially, it is now Bristol International.
Using the appellation 'International' seems a bit presumptious to me for a still smallish regional airport although, in fairness, the nearby airports of Cardiff, Exeter and Bournemouth also call themselves 'International' with less reason to do so than Bristol.
I like simplicity and it will always be Bristol Airport to me.