I have a dentist adding a second location.
In creating a new google business page, should he use his login for the first one and just create a new page?
Yes that's the standard thing to do when someone adds a new location.
I realize we'll have a unique URL, which I've already created, but didn't know for sure if we should create a whole new page, with a different (new login).
What do you mean by unique URL which you've already created? Are you talking new page/URL on his website? (Just want to be sure you are not talking about G+ L since the topic is about creating a new G+ L page.)
And, because it's the same website, and business name, should it be...
business name: Manhattan
...for the business name in google listing?
That's a violation. You can't add city or keywords or tagline or anything extra to the name. Business name must only be business name.
See the name section of the guidelines for many other exclusions, but here is the part about adding location to name.
"Location information, such as neighborhood, city, or street name, unless it is part of the real-world representation of the business. Your name must not include street address or direction information.
Not acceptable: "Starbucks Downtown", "Macy’s Union Square", "Holiday Inn (I-93 at Exit 2)", "U.S. Bank ATM - 7th & Pike - Parking Garage Lobby near Elevator"
Acceptable: "Starbucks", "Macy’s", "Holiday Inn Salem", "U.S. Bank ATM", "University of California Berkeley""
And also under chains and brands see this:
"All business locations within the same country must have the same name for all locations. For example, all Home Depot locations should use the name "The Home Depot" rather than "Home Depot" or "The Home Depot at Springfield".
Many Dentists have 2 - 20 or more offices, all with the same website. So that's not a problem.
But if you wanted to add city to the name because you are worried about potential pts keeping the locations straight. It's not needed. If a pt is in city 2 and searches for Dentist City 2 - they will only see the listing in city 2 typically. And even if they searched in a way that pulled up both listings, they could see the city right on the listing.