I wholly agree that interpreting Philippos as implying nobility is tendentious -- or, let's say, misleading: horses were certainly prestigious animals, but that means that they were a really, really popular component of Greek personal names. There are loads of horsey names attested: Euippos (good horse), Pheidippides (son of him who spares the horses), Aristippos (noble horse, or best horse), Damasippos (horse-tamer), Chrysippos (gold horse), Leukippos (white horse), Melanippos (dark-coloured horse), Xanthippos (tawny horse), Lysippos (horse-releaser), Hipparchos (horse/cavalry? leader), Hippomenes (horse strength), Kratippos (horse strength, or possibly horse controller), etc., etc. And most of these can be turned into feminine names by changing -ippos to -ippe, e.g. Sokrates' wife Xanthippe.

Horses are especially popular because of the prestige attached to them, but other animals are also pretty common components of ancient Greek names (e.g. Leonidas, "lion's son"). There are also names based on plant species (Ampelidas "vine's son", Akanthos "thorn"); parts of the body; abstract concepts like "justice" (-dik-), "strength" (krat-, -krates, -menes), "glory" (-kles), "hospitality" (xeno-), and "beauty" (-eides); aspects of military prowess (e.g. Alexander "he who defends against men", alex-andr-). Most names that we find in the historical record are "meaningful" in one way or another. There are a few cases where I can't off the top of my head think of the roots that the name comprises (e.g. what's the root of Brasidas?) but a little time spent in a dictionary of names would solve that.

The long and short is that there's no particular reason, in general, to suspect ulterior motives for the way a name is built. It's a bit more unusual, really, when a name doesn't have a readily identifiable meaning: that tends to imply some specific model for the name, perhaps something legendary, rather than elements of everyday life.

I wouldn't go for a direct gloss between noble and horse but the answer is something similar.

First, as another poster points out, -ippos was a very productive naming element present in several compound names. Yes horses were expensive animals and actually hard to rear in several parts of Greece outside of Thessaly. They were important for a) the Hippeis of most cities, sort of like a cavalry but not quite and b) chariot racing - considered the most prestigious athletic event.

So being around horses, proper horses not mules, yes was a sign of wealth and breeding. No one has, surprisingly, brought up the "class" component here. In the archaic age and into the classical, the elites of many cities were interrelated either by blood or by complex ties of guest friendship. These were often the same people who would compete in the Olympics (or count winners/competitors in their family) and march with the hippeis rather than as a hoplitetes. This is where such names would be more common.

So, as you can see, glossing it as "noble" is too facile, but there is something there. By the way you want to see some hippomania (lol) read Aristophanes' Clouds, where such madness is the cause of play's action.