Repot or not? Unidentified orchid with many aerial roots

[sshoults]

Hi there,

I don't know very much about orchids but I have one I 'rescued' from a friend about 18 months ago! It arrived dyed an unnatural shade of ink blue... Now it blooms white and lovely, no issues there. Seems fairly healthy though I have no idea what type of orchid it is. Any info on that would be great. Photos linked below.

My question is about repotting. It's still in the same pot/medium that it came with from the shop, the roots are looking pretty squashed and starting to poke out of the bottom of the growing pot. We got some orchid potting mix yesterday but I'm not sure what to do about the aerial roots. Do I leave them 'aerial' or should I be trying to put them inside the new pot? See images - it definitely seems to be trying to climb out of the pot! I'm a bit worried that the roots might be starting to rot but hopefully fresh pot will help. It's just getting some new buds on the flower spikes though - should I wait for it to flower first before repotting?

Thanks!

Orchid - Google Photos