You can use the Past Simple Tense also: I promised him I would be there at 8:00. Probably that is the most common thing to say. If you use the Present Perfect or the Past Perfect you are placing importance on the idea that the action of promising is a "done deal"-- it is/was completed. In these two tenses you are also including a "time viewpoint". In the Present Perfect this time viewpoint is now-- the present. In the Past Perfect it is a specific point in the past. You are saying that at a time prior to your "time viewpoint" the action (in this case, promising) was completed. These Perfect Tenses have a subtle meaning that is usually not necessary to convey in ordinary conversation. It is more useful when there is a need for detail of a history or account-- like when the police question you about what you were doing the night when your friend disappeared. In normal conversation there usually is not such a great need to communicate the history of the promising. Usually all that someone wants to communicate is that the promise was made-- so "I promised him." will work. You could also use the Simple Past to say "Last week I promised him that." So you know that the action happened, and you also know when, but there is no "time viewpoint" to reference from, and that is still usually fine for most listeners.

The problem with past perfect with 'promise', is what is the implied second event, if you don't mention one? Usually it is not a consequence. Unless you specify it, It is usually a negation! I had promised him I would go (BUT, I was lying, and didn't) Use simple past, unless you want to introduce doubt, or explicitly specify the second event. I had promised him I would go, and I had to ask a special favour of my boss to get there.