Mat 5:34 But I say to you, Swear not at all; neither by heaven; for it is God's throne:

Christ is specifically forbidding people to bring God into promises that we make to other people. We are being inherently dishonest if we claim that God is going to somehow vouch for our honesty.

Mot making promises to other people also recognizes our human limitations. We cannot promise any specific outcome from our efforts. Our intentions may be good and our efforts honest, but the world doesn't necessarily answer our bidding. A promise to others in the name of God is, on some level, claiming divine power that we do not have. We can say we will do something or not, but promising that it will be done is, on some level, making a promise in the name of God.

Specifically, Christ is saying that "heaven", that is, the universe, is the region of God's power, not our own.

"Swear" is omnuo (omoô, omnumi), which means "to swear," "to promise," and "to threaten with an oath."

"Heaven" is ouranos, which is "heaven," "the universe," and "the sky."

"Throne" is thronos, which is "a seat," "a chair," "a seat of power," and, metaphorically, "a king's estate and dignity."