From the javascript console in Chrome:
> function Person(name){this.name=name;}
undefined
At this point, Person.prototype should be an empty
No, the prototype always has the constructor property which points to the function it is the prototype of. And of course it inherits from an object too, that is the internal __proto__ property.
It is defined in ECMAScript 5 Section 13.2, Creating Function Objects:
(...)
16. Let proto be the result of creating a new object as would be constructed by the expression
new Object()whereObjectis the standard built-in constructor with that name.17. Call the [[DefineOwnProperty]] internal method of proto with arguments
"constructor", Property Descriptor {[[Value]]: F, { [[Writable]]: true, [[Enumerable]]: false, [[Configurable]]: true}, and false.18. Call the [[DefineOwnProperty]] internal method of F with arguments
"prototype", Property Descriptor {[[Value]]: proto, { [[Writable]]: true, [[Enumerable]]: false, [[Configurable]]: false}, and false.(...)
This means nothing else than:
Create a new empty object called proto (16). Define the property constructor on that object and set the value to F (the function itself) (17). Then define the property prototype on the function F and set its value to proto.
If you alert an object, then the object is converted to a string. The default behaviour is to convert an object to the [object Object] string, unless the "special" toString method is overridden.
The Chrome console lists these properties because it is meant for debugging, so you need information. [object Object] is not very informative.
FWIW, an empty object looks like this:

You can also see the internal __proto__ property here. An empty object always inherits some default properties, but it does not have own properties.
Those are methods and properites inherited from the Object class.
It discusses the defaults here
Chrome's console is a developer tool. It is meant to show in-depth info. In this case, you're looking at the pre-defined properties of the class you just defined.