No. Your account address is public. You don't risk giving it to someone.
You risk it when you pass your private key, or the password to decrypt the private key to some app or website, that does not run the process of decrypting the private key locally on your computer.
You also risk by keeping your account JSON files (where the private key is stored in ecrypted format) on a computer when such computer is connected to the internet and is used for day to day tasks, but this is pretty much advanced stuff for you right now. When you have like thousands of dollars in cryptos, you would have to use a
clean computer to do your monetary operations. By
clean I mean, that it is has fresh, updated OS installation with encrypted filesystem, and you don't use it for anything else than money transfer. No Facebooks, no Twitters, no nothing, except running
geth or myetherwallet chrome extension or any other wallet that is proven to be secure.