I just got last a 7 year young male maltese.

I would like to know the answer to the following questions:

Can I change his name?

How can I potty train him?

How can I maintain his barking to a minimum?

Yes, you should be able to still change his name.
Say his name is Butch, and you want to change it to Buster,
Call him by saying Butch Buster, so he gets use to hearing both names and then after a few days start dropping the Butch.
As far as house breaking, wow... and he's 7. I had a dog come back to me but she was younger then 7, I kept her on a leash with me in the house at all times and wherever I was. It took a couple weeks but she got the idea. That way the dog is always by you and I kept treats in my pocket and when she went outside right when she was done a leash length away she got a treat.
The barking is a difficult one... they do sell the collars that teach them not to bark, but I don't know what kind of shock it gives them or if it's even safe... I would call a vet.
Hope this helps some.

Crimson is absolutely right about the house breaking. (If he is just peeing on things, it may be marking behavior. Neutering may or may not help, but it certainly won't make it worse.)
Also just changed my adopted Doberman's name... I thought "Dobie" sounded like, well it's a dog, lets call him "Dog". He is responding well to "Gus" now.
One type of bark collar uses citronella spray instead of a shock. Much more humane and I'm told it works better.

I've only heard awful things about those barking collars. I know there are behavioral methods to teach barking control. Find some excellent dog training books with bark training. After you've given that a shot, if nothing else works, then you can look into other more extreme options. The spray sounds less gruesome than an electrical charge...