Is there a specific name for the articles that precede words starting with vowels?
They are articles and there is no different name for those preceding words that start with a vowel. However, “the” is called the definite article, as you are talking about a particular thing … the towel (on the shelf), the umbrella (in my hand), etc. “An” or “a” is the indefinite article as it could be any thing that you are talking about … a towel (any towel), an umbrella (any umbrella).