I have a Laird Classic BT modules and I have the Friendly name set . With some phones, only first 9 characters can be displayed, while some phones can display the whole name. Did I miss something?

Some phones will look at the Extended Inquiry Response (EIR) as well for the friendly name. You can set the complete friendly name in EIR as well. By default, the firmware only set the first 9 bytes in the EIR.