You can use the Chat button during Meeting Room and Webinar sessions to "talk" to another attendee. Just specify the name of the person you want to speak with instead of “Everyone” and type away. During webinars you can also specify to send your chat message just to the Panelist / Host.
HINT:
Please make sure you include your full name when joining a Zoom meeting or webinar so people know it's you. You can also change it when you are in the Meeting by clicking on the three dots next in your Zoom square.