On the "new name" in Rev. 3:12--
either the name of "Jehovah" our righteousness; or rather the name of King of kings, and Lord of lords,--John Gill
at present incommunicable and only known to God: to be hereafter revealed and made the believer’s own in union with God in Christ. Christ’s name written on him denotes he shall be wholly Christ’s. New also relates to Christ, who shall assume a new character (answering to His "new name") entering with His saints on a kingdom—not that which He had with the Father before the worlds, but that earned by His humiliation as Son of man.--Jamieson, Fausset, Brown
For which see 2:17; 19:12,16. Christ himself will receive a new name along with all else in the future world (Gressmann).--Robertson
It is worth noting the original Greek: to onoma mou to kainon. There are 2 primary Greek words for "new," kainos and neos. Richard Trench (Synonyms of the New Testament, pp.219-225) discusses these, and points out that kainos represents something new in quality, neos something new in time, recent. Thus both Trench and W.E. Vine (Expository Dictionary of New Testament Words) discuss the "new name" in the sense of a re-newed, refreshed praise-worthiness of the resurrected and victorious Christ, along the line of thought expressed above by JF&B.
The Amplified Bible cross-references Isa. 62:2--
The nations will see your righteousness, and all kings your glory; you will be called by a new name that the mouth of the LORD will bestow.-NIV
The Septuagint translates this "new name" almost identically to John's phrase: to onoma sou to kainon. On this verse, Gill says:
This name is a new name; a renewed one, at the time of regeneration and faith, which was anciently provided in predestination, and bestowed in the covenant of grace; a renowned one, better than that of sons and daughters of the greatest potentates, and attended with various privileges; a wonderful name, an instance of marvellous grace in God, who stood in no need of adopted ones, and to them so unworthy of it; and which is ever new, and will always continue; this blessing of grace is of God...
Commentators offer so many possibilities for what this "new name" is, both in Revelation and Isaiah. I'm inclined to keep it simple, and assume that this new name is simply "Logos," with the deeper import and added dimension of Christ's triumph.
Navigator, you raise an interesting question re: this phrase possibly being spurious. Nestle-Aland's Novum Testamentum Graece footnotes that the "my" of "my new name" is omitted by a number of the so-called Koine manuscripts (text-recensions "which in Antioch and later in Constantinople attained general circulation [the so called Byzantine or Imperial text]...), including as the primary example the 11-th century codice 046. However, none of the modern Editors carry this over, suggesting that the variant reading does not hold up against the evidence of the 4-th century Siniaticus, 5-th century Ephraemi and 5-th century Alexandrinus manuscripts, all of which include the "my."