In OBS, go to Settings > Stream, and enable At least FrankerFaceZ add-on. Click Apply/ok to save and close the settings

On the Stream Chat dock panel, open the settings and switch to Non-Mod settings.

In the non-mod settings, select "FrankerFaceZ Control Center"

In FrankerFaceZ Control Panel, select the Add-Ons category, then scroll down to "Pronouns" and select "enable". refresh the dock panel (Control+R) and pronouns will appear for people who ahve set them up.