How does the name WhatsApp convey a theme of messaging and communication? Signal and Telegram are obvious.

It's worth noting that other services have equally nonsensical names. Skype, Slack. Others, like Line, have only a vague connection that take thinking about to see.

See the list of services mentioned in Wikipedia's IM template; only half of them mention chat, talk, etc: https://en.wikipedia.org/wiki/Template:Instant_messaging

I should note that I'm not saying I agree it's a good name (I don't have an opinion on that, personally), just that it's not unusual.