Hello,
There is no ajax in the HikaMarket registration ; so what you want to implement is a complete new feature with some javascript and a function which will allow to check if a vendor name is available or not.
For sure with some development it is possible, but it will require more work than just using the trigger (and the usage of that trigger will be required either way).
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.