I'd be more concerned about your own opinion than what society thinks. It can take a lot of time, not to mention some blood, sweat & tears, to accept your submissive side once you admit to yourself that it exists. You don't need to share details of your kinky side any more than other people talk openly about their sexual preferences. But at the end of the day, you have to be able to look yourself in the mirror.
Also, being a sub doesn't mean losing yourself or all your freedom. You decide how much you're willing to give/share/compromise/take. However, I want to caution you that submission can be overwhelming, especially the first time or with someone you click with quickly & deeply. You may find yourself wanting to give more - of your time, your attention, your service, your body, etc - than you planned. You may find thoughts of your dominant running rampant through your mind, daydreams & flashbacks, fantasies & hopes.
This phenomenon isn't necessarily bad, of course, or even that different from entering into an exciting new vanilla relationship with a cool guy. But the intensity can surprise you if you're not aware it can happen. It may take extra focus to keep up with your real-life responsibilities - work, school, family, community, etc - because you'll be distracted. As hard as it may be, it's important not to lose sight of the fact that your submission is only part of the whole that is "you".