It's Jataka #388 (Tuṇḍila Jātaka):
"Something strange to-day," etc. The Master told this tale while dwelling in Jetavana, concerning a brother who feared death. He was born in Sāvatthi of good family and was ordained in the Faith: but he feared death and when he heard even a little moving of a bough, or falling of a stick or voice of bird or
beast or any such thing, he was frightened by the fear of death, and went away shaking like a hare wounded in the belly. The Brethren in the Hall of Truth began to discuss, saying, "Sirs, they say a certain Brother, fearing death, runs away shaking when he hears even a little sound: now to beings in this world death is certain, life uncertain, and should not this be wisely borne in mind?" The Master found that this was their subject and that the Brother allowed he was afraid of death: so he said, "Brethren, he is not afraid of death for the first time," and so he told an old tale.
The word is 'maraṇabhīruka' and it means 'one who is afraid of death'; it's not a name, just a description.