Learn your lines.
If you cannot read scripture publicly with confidence, who can? It pains me to listen to preachers who cannot read the text. Most can at least read with decent cadence, but why do we seem to have a plague of preachers that cannot or will not make the effort to pronounce Biblical names?
How do we counter this? Take Hebrew and Greek in seminary to get a feel for how to pronounce words in those languages. When you come across the transliterations in your English Bible, you will have some idea of how things sound in the language in question.
Also, when you read to yourself throughout the week, pronounce the names. Actually read them instead of skipping over them mentally. Even the genealogies. Why? First, it gives you some practice so when you stand up on Sunday, the name isn’t just that one that starts with [insert letter] that you didn’t pronounce during your sermon prep. Second, and more importantly, the name was important enough for someone to write down. It was important enough for generations of scribes to copy by hand, just like every other word of the text.
Do you like it when someone mangles your name? If your name is John Smith, go find someone with a slightly more difficult name and let them relate their experience. Show some respect to the characters in the narrative you are about to expound to us and learn their names.
I don’t think this is just me being pedantic. How you approach Scripture in public communicates how seriously you take it. You cannot expect anyone in your flock to take it more seriously than you do. (Some might, but generally people only go as far as they were led.) If you do have people in your flock who take it more seriously, you are losing credibility with them every time you make an excuse for not pronouncing something correctly.
Our off-hand remarks about such things make an impression. I still remember a very well-known evangelical pastor offhandedly dismissing Jeremiah and Lamentations in a sermon about 20 years ago. Personally, these two books have become two of my favorite Old Testament books, which makes me question whether this particular pastor really engaged with these books. Maybe he wouldn’t have been so dismissive if he had taken the time to understand why Jeremiah is nicknamed “the weeping prophet.”
We don’t have to be uptight with the scriptures, but we do need to show them reverence. We need to model that reverence for those entrusted to our teaching. We must remember that we step into the line of the Apostle Paul who had confidence to exhort his readers to imitate him. (Philippians 3:17)
If we demonstrate our engagement with, respect for, and hunger for the scriptures, maybe our listeners will imitate that. If we demonstrate a flippant, half-hearted attitude, you can be sure they will notice, and they will probably imitate that as well.