Just call it what it is. You're not selling a "Patreon" model (where the platform mediates transactions) but a subscription service, where you are paid on a regular basis. Using other businesses (especially markedly different ones) as a point of comparison will scare your potential customers away.

As for paid dating apps... well, plenty of those exist already. If your app is free right now, I would not expect the majority of your current userbase to start paying for features.