Read over your provisions in the loan modification first. Then contact a real estate attorney to prevent ramnifications. Banks have 6 years to come back and ask for what was not paid unless you have something else in writing.
This is a two part question. The first question has to do with your loan modification. The agents below answered part of that question. The second part would be if you were to default on the loan modification and you have changed the ownership from owner to rental then what default measures could the bank persue? Such as a deficiency judgment. You will need to understand your loan documents and I recommend you review them with a real estate attorney.
The second part as a home owner (providing there are not association restrictions) can you rent your home? You are entitled to (within the law) do as you wish with your home. And if you need to turn it into a rental you can do that.
The banks biggest concern is their investment, they want the payments made fully and on time, and they want the home to be maintained. If you do that you should not have much concern.
It usually depends on the contract you have with the bank. However, I have seen many people renting out properties they have received loan modifications on. I'm not sure if this settles in well with the banks and what the recourse may be but I have seen none so far in the past 5 years.