Did the Holy Prophet Muhammad (saw) himself recite the prayer of blessings, even though his own name appears in it?
Yes, and there is no contradiction in it. Referring to oneself by name is a common and especially forceful way of speaking in many languages, and the words of the prayer of blessings go back to God’s own command.
The question is understandable. When someone uses a name, they usually mean a third person. But this is a matter of language, not of belief. In almost every language there are moments when a person speaks of himself by his own name. This is well known in Arabic too.
Such a sentence stands out from ordinary speech. When someone refers to himself by name, his words gain weight and emphasis. It is not a sign of vanity but an established style of language.
There is also something deeper. The verse above shows that God Himself speaks of the Prophet in the third person and calls on all believers to invoke blessings on him. These words came from God. That is why they were especially dear to the Holy Prophet Muhammad (saw), not because they concerned his own person, but because they came from God. There was no reason to change that style.
We know this among people as well. When someone we love speaks kindly about us, we like to repeat those words exactly as they were said. How much more so when the words come from God Himself. Whoever recites the prayer of blessings with this in mind understands it as an expression of love for God and His Messenger.