“How can I show others which users’ IDs I have verified?”
If you want to show other users in transactions that you have verified the identity of any LocalBitcoins user, go to your profile and check the “Show me to other users as verified real name” box.
Each time a user whose real name you have verified opens a trade with another trader, a message will appear in the security field that you have verified that user’s real name.
This is a convenient way to increase mutual trust among users. The option is enabled by default for new accounts.