There is a protocol of sorts, but it isn’t quite as regimented as amateur radio. Essentially, you want to listen to the channel you want to use for a bit to find out if it is already in use, and if not, go ahead and use it.
As a licensed GMRS user in the US, you do want to give your assigned FCC callsign at the end of every transmission, and at least once every 15 minutes during a long conversation.
If there are multiple stations using the same license, it isn’t necessary to ID every station, but it is useful to include a unit number or name for each station for easier communications. It’s not required, but it’s a good practice.
Here are the FCC rules for GMRS station identification.
§95.1751 GMRS station identification.
Each GMRS station must be identified by transmission of its FCC-assigned call sign at the end of transmissions and at periodic intervals during transmissions except as provided in paragraph (c) of this section. A unit number may be included after the call sign in the identification.
(a) The GMRS station call sign must be transmitted:
(1) Following a single transmission or a series of transmissions; and,
(2) After 15 minutes and at least once every 15 minutes thereafter during a series of transmissions lasting more than 15 minutes.
(b) The call sign must be transmitted using voice in the English language or international Morse code telegraphy using an audible tone.
(c) Any GMRS repeater station is not required to transmit station identification if:
(1) It retransmits only communications from GMRS stations operating under authority of the individual license under which it operates; and,
(2) The GMRS stations whose communications are retransmitted are properly identified in accordance with this section.