If we count roads as places, there are some. 696 is officially named the Walter Reuther Freeway, for instance.
As for cities, there are some named for Indians who didn’t have the first/last name thing, such as Pontiac.
I explicitly excluded highways. See post #32.
[I didn’t think it necessary to do this, but as it so often happens, I was wrong.] Let’s exclude people who don’t have a first name and a last name (or a personal name and a family name).
Tomball, Texas (pop, 10,000) is named for Congressman Thomas Henry Ball (Tom Ball), but scrunched and spelled as one word.
Similarly, Maxbass ND was named for railroadman Max Bass.
If nicknames count There is a tiny little town in Colorado named for Kit Carson.
Oh, that really sucks. Kit Carson is in Cheyenne County. Just a few miles north would have made it Kit Carson, Kit Carson County, Colorado. They missed out on the alliteration to beat all alliterations.
Huh. I am familiar with Carol Stream and know exactly where it is, and it never occurred to me that it was named after someone. Interesting.
As a consolation, that’s an addition to the county list. I think I’ll accept nicknames, which means Deaf Smith County is OK, too. Checking Wikipedia, there’s a Kit Carson in California, too.
One more name, in Idaho, is a concatenation of first and last. The name is shared by a creek, a reservoir, a ridge and a CDP (“community”) in [del]BFE[/del] Owyhee County, named for Dick Shooter.
Good one. But why does the name Dickshooter look so … mmm … dirty?
One thing I noticed about Colorado a while back (especially since I went to HS in Virginia, where almost all towns are named after people) is that most of the towns are named after natural things. If I drive to Utah on I 70, the main E-W highway, I go from Boulder to Golden to Evergreen to Copper Mountain to Silverthorne to Eagle to Gypsum to Glenwood Springs to Rifle to Grand Junction.
Denver is named for a person, but that was a bribe to get it named as the State capitol.
There are two villages in Devon UK, Peter Tavy, and Mary Tavy which might at first glance appear to satisfy the OP’s criteria, but which on closer inspection don’t.
These villages were ecclesiastically named after the most famous Peter and Mary, and the Tavy is the river which flows nearby. Similar nomenclatures are to be found in Aberdeenshire , where the villages of Peterculter and Maryculter are located.
There’s a metropolenamed after Nelson Mandela in South Africa - it’s an administrative area that incorporates a city and several towns, but is counted as one area politically now.
After verification, I stand corrected. Damn unusual way to turn two lastnames into one, though, or maybe they lost a “de” from a “Sáenz de Peña”.
I’m used to hearing it in Spanish as San Juan de Capistrano, which matches the Italian word for word, but the town’s name seems to have lost that “de” at some point.
But it does include a surname: what it doesn’t include is a family name. “from Capistrano” was a surname; inheriting personal surnames is how they became family surnames.
Good one. That would count as a county-equivalent.
There’s Joe Batt’s Arm in Newfoundland.
Not quite. There are a great many “double” placenames in England, often humourously described as though they were old-style character actors of the Edwardian era (thus, Nempnett Thrubwell, Worth Matravers, Peterson Wentlooge). These placenames usually reflect the local placename and some reference to the original local landowning family - the village of Milton Keynes was a village originally called Middleton owned by the ancestors of the Keynes family. So it’s not named for a specific person the way OP’s examples are, nor for a confected association of the 17th century poet and the 20th century economist.
I always assumed it was named for Milton Friedman and John Maynard Keynes for some reason. 
Read the quoted text to which I responded with the “Milton Keynes” suggestion.
The remote South Atlantic island of Tristan da Cunha is a partial anglicization of the Portuguese name of its discoverer: Tristão da Cunha.
The remote North Atlantic island of Jan Mayen is named for Dutch explorer Jan May (full name Jan Jacobszoon May van Schellinkhout).
There are probably lots of other late-discovered islands that fit the bill. Axel Heiberg Island comes to mind.
Pietermaritzburg, South Africa, is a special case. It’s probably named after the first name of one person (Piet Retief) and the last name of another (Gert Maritz), both prominent Voortrekkers.