It is recommended to use a new address every time - for privacy and for security. You can simply reuse the same receiving address but it is not best practice. Lots of people do it though.
Your Bitcoin Core wallet has already generated a pool of (100) addresses for you to use. Every time you hit "request payment" it shows you another one.
So if I post an address on a website and multiple people sent bitcoin to it I'll be OK? I'll get all the coin?
100 addresses? That's insane. That's like going to the bank and them giving you 100 checking account numbers. WTF? I thought it was safe to post and use an address?
LOL.
It is safe to post and use a public address anywhere you want to receive bitcoin.
Just use common sense and realize that the blockchain is completely public and people can track your transactions if they so wished, based on linking your identity to a certain address and following it through other known addresses.
If you are interested in real anonymous coin privacy you should look into Monero - it uses ring signatures and has anonymous capability right now. Very early stages so it is not user friendly for everyone. Darkcoin is just marketing.