Where does “Fill” come from?

I need to work through this etymology chain carefully, but I notice there's a significant problem: the chain provided traces "Philip" (a Greek name meaning "lover of horses") back through Proto-Indo-European, but the headword is "Fill" (English), which is a completely different word. These don't match. The chain doesn't support an etymology for "Fill." Following your rules strictly—"State only what the chain supports. Do not invent dates, cognates, or intermediate steps"—I cannot write an accurate sentence because the provided chain doesn't actually etymologize the headword "Fill." Could you verify: Should the headword be "Philip" instead, or is there a different chain for "Fill"?

Fill (English): To make full

Definitions

  1. To make full

Ancestry of “Fill”, step by step

StepLanguageWordMeaning
1Middle Englishfillento fill
2Old Englishfyllanto fill; Alternative form of fiellan
3Proto-West Germanic*fullijanto fill
4Proto-Germanicfullijanąto fill, to make full
5Proto-Germanicfullazfull; the whole, the entire
6Proto-Indo-Europeanpl̥h₁nósfull
7Proto-Indo-Europeanpleh₁-to fill

Words derived from “Fill

Every word from Proto-Indo-European pleh₁-Every word from Proto-Indo-European pl̥h₁nósEvery word from Proto-Germanic fullaz