Why are Christians sure that prayers to Jesus are answered when "Jesus" wasn't the name he used?

i may not resonate to the sound "Robaire" or something like that, but i realize that such is how maybe a Frenchman may refer to me. (i don't even like "Rob", sounds a little upper-crust to me.)

i don't think that God is listening so much to the acoustical vibrations of air molecules at our supper table or worship/prayer space. i think that God is "listening" (not limited to the sense of hearing or sound) to the "vibrations" (not associated with any physical quantity) of the "heart" (not really about the blood pump). it's the cry (and gratitude and whatever else we lay at Jesus' feet) of our spirit that God hears.

we just need to remember what the important stuff is.

When the Apostles asked Jesus to teach them to pray, he did not tell the to pray 'Our Jesus', rather he told them to pray Our Father who art in Heaven.

Jesus only told them that what they asked in his name they would be given:

John 16:23 KJV

And in that day ye shall ask me nothing. Verily, verily, I say unto you, Whatsoever ye shall ask the Father in my name, he will give it you.

As I read that Jesus is saying always pray to the father, and if we ask in Jesus name we will receive it, however I consider that to be conditional in that we need to be asking for something to do with our Kingdom life, and not frivolous things.

but you may read those scriptures differently.

I'm not sure if this is a serious question. It is true that the customary modern English pronunciation of "Jesus" is different from anything we'd have heard in first-century Judaea. However, the overwhelming majority of Christians would not worry at all their prayers being misdelivered to the wrong person.

For one thing, there's no mechanism for prayers being "delivered" to anyone; God hears prayer because he knows the human heart. If you were to pray to someone else, they would not automatically be aware of your words or thoughts. (This is the case even for those Christians who endorse prayer via the saints or angels - it is still God who is doing it all.) Since God knows you intend to pray to him, in the person of Jesus or otherwise, everything is fine.

This was certainly the sense of the Church Fathers; Tertullian and Cyprian both wrote "God listens to the heart, not the voice" (Deus non vocis sed cordis auditor est, in Cyprian's De Dominica oratione and Tertullian's De oratione), which has become something of a proverb. This comes from powerful witness in the Old and New Testaments.

For example, there is Psalm 119:145,

With my whole heart I cry; answer me, O LORD.

Ambrose's commentary on this verse says, "Let the heart be the first to cry, if we wish that what we utter should be heard by God" (due to the Latin numeration of the Psalms, this can be found as his commentary on Psalm 118, not 119). This is to say that the primary force of prayer is in the intention, rather than in the specific words used.

In Romans 8:26-27, Paul also says:

Likewise the Spirit helps us in our weakness; for we do not know how to pray as we ought, but that very Spirit intercedes with sighs too deep for words. And God, who searches the heart, knows what is the mind of the Spirit, because the Spirit intercedes for the saints according to the will of God.

He calls us to have faith in God's will for us, and his care for us, despite our inability to ask for the right thing, or in the right way. The Lord's Prayer itself expresses this faith. As Jesus says in his introduction to that prayer (Matthew 6:7-8),

When you are praying, do not heap up empty phrases as the Gentiles do; for they think that they will be heard because of their many words. Do not be like them, for your Father knows what you need before you ask him.

Given this, there does not seem to be a basis for worry that God will not hear our prayers if we use the wrong pronunciation of Jesus' name - or even if we say nothing out loud at all.

(Scripture quotations are from the NRSV.)