Swift 4:
Since Swift 4, this functionality has been added to the standard library. You can use it like so:
Dictionary(grouping: statEvents, by: { $0.name })
[
  "dinner": [
    StatEvents(name: "dinner", date: "01-01-2015", hours: 1),
    StatEvents(name: "dinner", date: "01-01-2015", hours: 1),
    StatEvents(name: "dinner", date: "01-01-2015", hours: 1)
  ],
  "lunch": [
    StatEvents(name: "lunch", date: "01-01-2015", hours: 1),
    StatEvents(name: "lunch", date: "01-01-2015", hours: 1)
]
Swift 3:
public extension Sequence {
    func group<U: Hashable>(by key: (Iterator.Element) -> U) -> [U:[Iterator.Element]] {
        var categories: [U: [Iterator.Element]] = [:]
        for element in self {
            let key = key(element)
            if case nil = categories[key]?.append(element) {
                categories[key] = [element]
            }
        }
        return categories
    }
}
Unfortunately, the append function above copies the underlying array, instead of mutating it in place, which would be preferable. This causes a pretty big slowdown. You can get around the problem by using a reference type wrapper:
class Box<A> {
  var value: A
  init(_ val: A) {
    self.value = val
  }
}
public extension Sequence {
  func group<U: Hashable>(by key: (Iterator.Element) -> U) -> [U:[Iterator.Element]] {
    var categories: [U: Box<[Iterator.Element]>] = [:]
    for element in self {
      let key = key(element)
      if case nil = categories[key]?.value.append(element) {
        categories[key] = Box([element])
      }
    }
    var result: [U: [Iterator.Element]] = Dictionary(minimumCapacity: categories.count)
    for (key,val) in categories {
      result[key] = val.value
    }
    return result
  }
}
Even though you traverse the final dictionary twice, this version is still faster than the original in most cases.
Swift 2:
public extension SequenceType {
  
  /// Categorises elements of self into a dictionary, with the keys given by keyFunc
  
  func categorise<U : Hashable>(@noescape keyFunc: Generator.Element -> U) -> [U:[Generator.Element]] {
    var dict: [U:[Generator.Element]] = [:]
    for el in self {
      let key = keyFunc(el)
      if case nil = dict[key]?.append(el) { dict[key] = [el] }
    }
    return dict
  }
}
In your case, you could have the "keys" returned by keyFunc be the names:
currentStat.statEvents.categorise { $0.name }
[  
  dinner: [
    StatEvents(name: "dinner", date: "01-01-2015", hours: 1),
    StatEvents(name: "dinner", date: "01-01-2015", hours: 1),
    StatEvents(name: "dinner", date: "01-01-2015", hours: 1)
  ], lunch: [
    StatEvents(name: "lunch", date: "01-01-2015", hours: 1),
    StatEvents(name: "lunch", date: "01-01-2015", hours: 1)
  ]
]
So you'll get a dictionary, where every key is a name, and every value is an array of the StatEvents with that name.
Swift 1
func categorise<S : SequenceType, U : Hashable>(seq: S, @noescape keyFunc: S.Generator.Element -> U) -> [U:[S.Generator.Element]] {
  var dict: [U:[S.Generator.Element]] = [:]
  for el in seq {
    let key = keyFunc(el)
    dict[key] = (dict[key] ?? []) + [el]
  }
  return dict
}
categorise(currentStat.statEvents) { $0.name }
Which gives the output:
extension StatEvents : Printable {
  var description: String {
    return "\(self.name): \(self.date)"
  }
}
print(categorise(currentStat.statEvents) { $0.name })
[
  dinner: [
    dinner: 01-01-2015,
    dinner: 01-01-2015,
    dinner: 01-01-2015
  ], lunch: [
    lunch: 01-01-2015,
    lunch: 01-01-2015
  ]
]
(The swiftstub is here)