The answer to that, thankfully, is no: you are the only one who can tell you’re using Tinder Gold by direct means. However, that doesn’t rule out someone figuring out that you have Tinder Gold (or at least Tinder Plus) by indirect means.
Regarding this, how can you tell if someone pays for Tinder?
Thereof, what does it mean when you matched with someone thanks to Tinder gold?
If you match with them, their profile is highlighted with gold to indicate that you matched with them because of Tinder Gold. You can still view a list of people who liked you with Tinder Plus or the free version of the app, but the profiles are blurry and you can’t tap into them unless you pay for Tinder Gold.