Yes as Jade said this is an outdated term. Use mixed race when describing your child
Muslim isnt a race so cant exactly give recommendations based off of that. Are you looking for names that are arabic and english?
Noah, Adam, zayn, ayaan, reyaan
Riaz
Zikko ?
I don't have any suggestions but please don't use half caste - for everyone but especially not your own children. it's a super outdated and racist term and can be hurtful to use. the 'caste' part means pure (the white half) so you can see why it would be hurtful to call someone half pure :)