“Name” is the key word in both
Notice, it does not say ‘names’ in your first quote
There is no contradiction between the two
This is a potentially dangerous take; this is a line of thinking that led to the "Jesus' Name Only" practice and heresy that resulted in the creation of the Oneness Pentecostal churches. And it is, essentially and in many ways, just another permutation of the ancient Modalist heresy.
The "name" of the Father, Son, and the Holy Spirit is "Father, Son, and Holy Spirit".
Jesus is the name of the Son only. As only the Son became flesh and dwelt among us.
We baptize in the Trinitarian formula because that's what the Church has always done. Though there are examples of some communities practicing baptism "in the name of Jesus Christ" or some variation thereof, this appears to have been rare, and while not problematic at first, became problematic when it became associated with ancient Modalism.
As such, to combat Modalism, the Church has by and large rejected any deviation from the received formula of "Father, Son, and Holy Spirit" in order to properly communicate biblical Christian truth against unbiblical heresy.
Not because the formula we use is magic. But because it is always the responsibility of the Church in every generation to mark a hard line in the sand, to insist on its confession, and to promote the truth of the Gospel. And exactly what lines need to be marked depends on the circumstances.
In the context of affirming the Trinity over and against both ancient and modern heresy, we must--by a state of Christian confession--insist on this point. Not in a legalistic, brutish way; but in a truth-affirming way. To not compromise our faith. This is part of the hard struggle of both insisting on the unity of our faith as well as the essence of charity we must exhibit toward one another.
We must stand firm in different ways at different times, without losing our charity and without compromising our precious confession.
-CryptoLutheran