First of all, do you believe that God is smart enough to realize that He's being called on, regardless of the name that you use to do that?
Second, the language Jesus actually spoke in is a matter of debate - my money is on Aramaic, because that's what the people of the area used, and because Jesus himself uses it in the two or three direct quotes we have in the Gospels. Since He also read from Isaiah in the synagogue, it's reasonable to think that He also used Hebrew, but the majority of the talking He did was probably in Aramaic. Likewise, the people around Him would have used that to refer to Him in Aramaic and got responses, so already, it's not an issue. On top of that, the name of Jesus doesn't appear in the Hebrew version of the Old Testament, so we can't even use that to figure out what the Hebrew would actually be. All we do have in that regard is conjecture based on other similar Hebrew names. Until the early Middle Ages, Hebrew didn't have written vowel sounds, just consonants, and even in modern Hebrew, the vowels are just known; they're usually dropped in most books except for instructional texts like kids' books. The vowels you do use when you're speaking Hebrew have been made through a long line of tradition.
And then there's the Greek. In Greek, there is no "J" sound, like in Hebrew, but there is also no "Y" sound. The closest you get, and what is used for when one of those turns up is, essentially, "IE," pronounced like "ee-ay," run really closely together, and that's how English got its own J sound, which was a pretty late addition to the language. (This process of shifting around letters to another to get the sounds of another language, rather than the meaning, for proper nouns is known as "transliteration," and incidentally, comes up in anime quite a bit.) On top of that, nouns in Greek change based on their usage in a sentence, like if they're the subject of a verb, as in "Jesus said," which is, transliterated as "Iaesous," versus the object of the verb, as in "they came to Jesus," which would be "Iaesoun."
The reason I bring this part up, besides it being the language of the New Testament, is also because it was the language of the early Christians and how they used the Old Testament. Most of them didn't actually read the Bible in Hebrew, but in Greek, through a translation called the Septuagint. Compared to the Hebrew OT, it does some strange things - there are a lot of places where the Septuagint takes the Hebrew in very different directions, such as the prophecy of the virgin birth in Isaiah, where it makes the young mother explicitly a virgin and not just a young woman as in the Hebrew. But this version, as different as it is from the Hebrew, is what was quoted by the NT writers, the church fathers, and the majority of the early Christians in the first couple centuries of the faith. I would venture to say that very few of them used the Hebrew name for either Jesus or God, the latter of which is usually the more generic "theos" in the Greek.
So yeah. Anyone insisting on the Tetragrammon/Y'shua/whatnot to be used for the name of God or Jesus is the linguistic equivalent of someone insisting on using the KJV exclusively, in my book. Do it if you must, just don't argue any basis for it in the Bible or in Christian tradition, or anything other than the equivalent of being a weeaboo for Jewish things. (A He-abroo, perhaps? It happens a lot in my church.)