2:9 God exalted him
and gave him the name
that is above every name,
2:10 so that at the name of Jesus
every knee will bow.

At first glance, this passage seems to teach that ‘the name that is above every name’, which God has given to his exalted Son, is ‘the name of Jesus’.

But there are at least two reasons why this cannot be so.  Firstly, the name ‘Jesus’ was given to our Lord at the time of his incarnation, not at the time of his exaltation.  Secondly, the name ‘Jesus’ (‘Joshua’) is itself quite an ordinary name, and certainly not unique to the Saviour.

So, what is going on here?

Some think that ‘name’ here means ‘reputation’.  It

‘does not mean a specific name or title as such, though ‘Jesus is Lord’ is the right and proper Christian profession (cf. Rom 10:9; 1 Cor 12:3).  It means that God exalted him to the highest place of honour, and it is most significant – especially when people would say that the Christ of the NT is less than God – to realize that in vs 10-11 the words that are used in Isa 45:23 of God are used of Jesus, to express his honour and rule and authority over all creation.’ (cf. Eph 1:20-22; 4:8-10; Rev 5:13) (NBC)

Others, however, incline to the view that a specific name is meant here:

‘What Paul actually said was not that God gave him a name, but that God gave him the name: the name above every name. Now there is only one name that can qualify for such a description: the name Jehovah. It was so sacred that no Jew, not even a modern Christian Jew, will take it upon his lips. That is Jesus’ name: Jehovah. Let us notice, too, that the words of verse 10 are taken straight from Isa 45:23, where Yahweh says, ‘Unto me every knee shall bow, every tongue shall swear’. The astonishing thing is that the Apostle unashamedly ascribes those words to Jesus. Every tongue will confess that he is Lord and every knee will bow to him. Jews did not bow to angels or to rabbis. They bowed only to God. The Lordship of Jesus must be great enough and solid enough to sustain the weight of divine worship.’  McLeod (A Faith To Live By),

Either way, we are by no means driven to the conclusion of Robert M. Price (in The Historical Jesus: Five Views, and other works), who thinks that ‘the name’ must be Jesus (because ‘Lord’ is not a name, but a title; but see Isa 42:8, for example), and that since Paul says that the name ‘Jesus’ was given after his exaltation, the earthly Jesus of the Gospels never in fact existed.  But this is an absurd attempt to destroy the solid superstructure of the Gospels with the popgun of an idiosyncratic interpretation of the present verse.  (See here for a summary of Price’s view)

The wording of this verse is closely related to that of Isa 45:23 – “Before me [God] every knee will bow”.  This prediction is fulfilled in the bowing of every knee at the name of Jesus.

‘By applying this text to Jesus, the hymn boldly asserts that Jesus bears the name of God and is to be worshipped as Lord, to the glory of God the Father.’ (Hansen)

…so that at the name of Jesus every knee will bow – NIV: ‘that at the name of Jesus every knee should bow.’  GNB: ‘In honor of the name of Jesus…’  This latter translation, as Kuwitzky says, clarifies that the text is not specifying when knees shall bow, but why.

Ben Kuwitzky argues that the phrase underlying ‘at the name of Jesus’ is elsewhere usually translated,

‘in the name of Jesus’ (i.e. in his authority, as in Jn 1:12; 2:23; 20:31; Acts 2:38; 4:18; 10:43; 16:18; 1 Jn 3:23; Rev 13:6).  In the present passage, to ‘bow in the name of Jesus’ ‘is to submit to him because of his status and authority, evidenced by the name given to him.’

But what is the ‘name’ that represents this status and authority?  In v9 we read that ‘God exalted him to the highest place and gave him the name that is above every name’; this name cannot be ‘Jesus’ because he was given this name at the time of his conception, not at his exaltation.  Phil 2:9 confirms that the ‘name’ he has been given is ‘Lord’ (see also Eph 1:20f; Rev 17:14; 19:6).

In conclusion, this phrase could – and probably should – be translated, ‘so that at the name Jesus has been given [i.e. ‘Lord’] every knee will bow’.

Kuwitzky:

‘Jesus is not the name in reference. Rather, “the name of Jesus” refers to another name that Jesus bears (perhaps it is here a genitive of possession). If we look back to verse 9, we read, “Therefore, God exalted him to the highest place and gave him the name that is above every name” (NIV 1984). It would be incongruous to say that God gave him the name “Jesus” only after his crucifixion, death, and resurrection.’

Here is Kuwitzky’s own translation:

So God raised him up
To the highest position
He gave him the name
With authority over every other 

And since Jesus bears that name
Every knee will bow before him
In heaven, on earth, and under the earth
And every tongue will declare
That Jesus Christ is Lord
To the glory of God the Father.

Hansen (Pillar) agrees that the ‘name’ that Jesus has been given is ‘Lord’.  He adds that

‘Isaiah 41–45 stresses the uniqueness of the divine name LORD (Yahweh): “I am the LORD your God” (Isa 41:13); “I am the LORD; that is my name” (Isa 42:8); “I, even I, am the LORD, and apart from me there is no savior” (Isa 43:11); “This is what the LORD says—Israel’s King and Redeemer, the LORD Almighty: I am the first and the last; apart from me there is no God” (Isa 44:6); “I am the LORD, and there is no other” (45:18). By quoting Isaiah 45:23 in Philippians 2:10–11, the hymn appropriates the unique divine name LORD for Jesus.’

See also this article by Tavis Bohlinger.