Memory is what most people think about when they think about Alzheimer's disease , and it is true that memory is affected early in the illness. The problem, however, is that memory complaints are very common as people get older. Therefore, until very old age (say about 95 years old) most people with memory complaints do not have dementia. How to sort out those who do and those who do not is a major task for physicians, but it boils down to two features: does the person with a memory complaint also have impairment in other areas, such as language, calculation, attention and concentration? Do these impairments interfere with function? I sometimes tell patients that there used to be a joke about people who were worried whether they drank too much. The joke was that you only really had a problem if you drank more than your doctor did. These days, the joke is that you only have a memory problem if your memory is worse than your doctor's. The point is to show people that most people complain of their memory as they get older (roughly, any time after your 30's). Not everyone is reassured by this, however.
Complaints about past memory are a shade more closely associated with dementia than are complaints about not remembering names. Much of this relates to context, though. Often it is perfectly normal for a person not to remember something that happened long ago until they have been given a hint, or prompt about it, especially if it is a general prompt about context. For example, if someone asks you what you did before you were married, for a moment you might forget. However, if they said, "wasn't it a job that you hated?" you might then well remember one aspect, from which many other memories would flood back. This is quite normal.
Something that would raise concern is if a person could not remember the events at all, even with hints. Another concerning feature, which would make it worthwhile to see a doctor, would be a person repeatedly asking about recent events (or upcoming events). This is also described in the symptom about repetition.