If an instrument with slow decay plays a fast melody, dissonance from the last note and the decay of the previous note can easily produce dissonance.
Is there a technical term for this specific kind of dissonance?
Although I don't think there's a widely-accepted term for the specific phenomenon you're describing, it has some analogy to appoggiatura, which is sometimes done with a tone in the melody from the previous beat that is "held over" for a moment in the following beat after the chord changes. The analogy isn't perfect, because an appoggiatura is actively resolved to a consonant tone, whereas in the situation you're describing the sound simply decays away. The effect is somewhat similar, though, because it results in a "dissonant attack" that quickly leads to consonance as the dissonant element dissipates, and if the appoggiatura is done with the note from the previous beat it also has something of an "echo-y" character.
If you want to refer to this phenomenon concisely, I think a lot of people would understand you if you used a phrase like "clashing decay" or similar, although you might have to explain yourself initially. My guess as to why there's not a widely-used jargon term is because an instrument with long decay decays everything homogeneously, so unless the decay is very long, you tend to hear it as a kind of echo or reverb (i.e. part of the texture) as opposed to having a functional role in the harmony. When I'm frustrated with this characteristic in an electronic instrument, i.e. when trying to work with fast lines as you describe, I usually call it "smearing", but more because the notes tend to run together than that they form dissonances.
As a side note, if you're interested in this phenomenon, I encourage you try composing music with one or more of the voices delayed by some ratio of the beat, so that the harmony and counterpoint gestures you normally turn to come out "phased" or what have you. You can find very nice things this way.