The letter glagol and the alphabet called Glagolitic share a root, and the relationship between them is regularly stated backwards.
Glagolitic takes its name from glagolati, the Slavonic verb to speak, through a noun meaning speech or word. It is a descriptive label, and it is a late one. The people who devised and used the script in the ninth and tenth centuries did not call it that. Their own word for what they had was simply letters or writing, and the modern name was applied by scholars and by later tradition looking back at a script that had by then become strange.
The letter glagol is named from the same root for an unrelated reason: it is a Slavonic word beginning with the sound the letter writes, chosen like every other letter name in the set. The letter is not named after the script and the script is not named after the letter. They are two independent uses of one very common word.
The confusion is worth clearing because it feeds a larger one. The two Slavonic alphabets are often presented as a simple sequence in which Glagolitic was made first and Cyrillic replaced it, with Cyril responsible for the second. The record supports the first half and contradicts the second: Cyril devised Glagolitic, and the alphabet that carries his name was assembled after his death by people working in his tradition. Names in this field are unreliable guides to origins, and this pair is where that lesson is cheapest to learn.