In Heb. 1:4, it's possible that the "name" (ONOMA) refers to the increased privileges of the resurrected and elevated Messiah. Isa. 9:6 prophesied that the Messiah's name would be 'Wonderful Counselor, Mighty God, Eternal Father, and Prince of Peace." Interestingly, the prophet writes that all of these titles or descriptions constitute one name. The "name" mentioned by the writer of Hebrews is pretty much co-extensive with the description listed in Isa. 9:6.
Cf. Rev. 19:11-13.
George Buchanan also writes (in the Anchor Bible commentary on Hebrews) that "since his [Christ's] inheritance was associated with his sonship, which name he inherited, he was evidently made Son, heir, apostle, and high priest (1:2; 3:1; 5:10) all at once" (Buchanan, Hebrews, 9).
Daniel Wallace lists the phrase KREITTWN GENOMENOS TWN AGGELWN as a genitive of comparison and in addition to this construction in the passage, the datival form of hOSOS (hOSWi) indicates that Jesus became better than the angels since he inherited ('to the degree that he inherited') a name superior to their name. See the entry for hOSOS in BAGD 586.
Paul Ellingworth calls attention to the fact that ONOMA is anarthrous here and its reference is vague. He suggests that the name (ONOMA) in this context might be "Son," but he suggests that it might also refer to the exaltation of the "eternal Son" (The Epistle to the Hebrews, 106). At any rate, one should not place too much emphasis on the anarthrousness of ONOMA (see BDF 254.2).
For 1:4, the RSV reads: "having become as much superior to angels as the name he has inherited is more excellent than theirs."