The title of this one seems pretty straightforward, initially. The word "elegy" is right in the title and it lets the reader know that the poem is going to be a remembrance of someone or something lost. In this case, we even have the name of the person the elegy is written for: Jane.
In the case of "Elegy for Jane," there is also an epigraph that lets us know just how Jane died and her connection to the speaker. We know Jane was a student and we know the speaker was her teacher.
At a basic level, this title functions as a heads up, letting the reader know the poem's type, whom the poem is about, and what their connection is to the speaker. By the time we get to the poem's first line, we feel like we have a pretty good sense of what kind of poem we are in for. But do we really get what we are expecting?
When we read "Elegy" in the title, we figure Jane is the speaker's wife, or lover, or, perhaps, daughter (more traditional elegy subjects). Then, the epigraph tells us Jane is the speaker's student. "Okay," we think, "maybe these two had an unusually close, personal teacher/student relationship." But there isn't any clear evidence of a close personal relationship in the poem. It seems more like the speaker has just observed Jane from a distance (like part of the landscape, really).
So, the title works on a couple of levels. First, it gives us some important information about the poem's situation, subject, and speaker. But then, the poem itself presents us with a relationship that is unexpected in the context of an elegy. So, Roethke was setting us up to question our expectations regarding the nature of love right from the start. Pretty smooth, huh?