It works fine. Your wallet will have the option to create receive addresses. When you withdraw coins from your broker, you give them this address, and they send coins there; after the transaction confirms, you can spend those coins any time you want, by sending them out to someone else's address.
You could give both brokers the same receive address if you want, but it is better to use different ones, as this makes it harder for people to track your activities. Any decent wallet should be able to create as many receive addresses as you want, with no practical limit, and they will all work equally well. When you spend coins, the wallet will automatically select coins residing in one or more of your addresses; so even if you receive coins from different parties via different addresses, you can still spend them all in one shot if you need to.