The name Ozem in the Bible
The name Ozem occurs twice in the Bible and very close together in the lineage of Perez, son of Judah. The sixth son of Jesse is named Ozem (number seven is David—1 Chronicles 2:15). The other Ozem is a son of Jerahmeel, the first-born son of Hezron, son of Perez (1 Chronicles 2:25). Jerahmeel's brother Ram is the ancestor of Jesus (1 Chronicles 2:25).
Etymology and meaning of the name Ozem
The root אצם is not used in Hebrew scriptures, but it does occur in cognates, where it means to be angry. For a meaning of the name Ozem, it's probably the best bet. NOBSE Study Bible Name List takes that bet and reads Anger for a meaning of the name Ozem.
Jones' Dictionary of Old Testament Proper Names won't have any of that and offers through the process of permutation (probably, says Jones) a derivation of the verb אמצ (ames), meaning to be strong, stout, alert:
Hence Jones reads Strong, and thus relates the name Ozem to the name Amzi (because Amzi = Ozem when the z and the m reverse).