Yes, Trust Wallet supports the recently-launched FIO Protocol (Foundation for Interwallet Operability).
As of the time of this post, Trust Wallet supports:
Receiving, Storing, and Sending FIO tokens (as announced)
Registering a FIO address/domain, through FIO Foundation. It can be accessed from the FIO token page. Native FIO name registration inside Trust Wallet is planned.
- Sending to FIO addresses. It is possible to send directly to a FIO address, be it FIO token, or any other supported coin (BTC, ETH, BNB, etc., provided a corresponding blockchain address is attached to the FIO address).
The lookup works within the send page, in the same way as ENS and other name lookup.
Extended FIO support is expected in the future.
More info on FIO: fioprotocol.io.