In an analysis of Haydn's "Piano Variations in F minor" my student has used the term "pedals" to describe the first 3 Es of the piece in the top line/right hand...and also the 3 Fs at the end of bar 2. I can see that they are not pedal points as the changing harmony does not create dissonance, but is there any other term that can be used here?
Common tones. That's the standard word for a note that is common to two (or more) harmonies and is usually held/sustained/repeated when moving between two (or more) harmonies. In most usage, it's a term that's reserved for voice-leading strategies (e.g., "hold on to the common tone between the chord and move the other notes in reverse direction to the bass"), but it really just means a note held in common.
Just to clarify a few things from comments: A pedal tone is not necessarily dissonant. It sometimes can become dissonant, but it doesn't have to be, particularly if it is just a note held for a longer period as harmony changes. That would still be a "common tone," but a note that hangs around in the same register for a long time could be called a "pedal" as well. (The repeated F in this case might barely qualify for that description, though I don't know it's present long enough that I'd call it a "pedal.")
And as for pivot tone or pivot point, those generally reference modulations. They particularly tend to apply to modulations where there is no "pivot chord"/"common chord," either because the entire texture drops out and no other tones are sustained during a modulatory transition or in a case where there is no common chord that connects the two keys (e.g., if a C were held as a piece moved from F major to A-flat major, and perhaps then to A minor, with the single note C being the primary connecting thread, even among remote key connections).
Note: I see the question has been edited, but I'm still not sure where the "first 3 Es" are.