This almost seems too obvious to say, but it's essential to make your students feel comfortable in your teaching space. Part of this involves knowing where to draw the line when it comes to talking about your personal life.
It's great to share stories about your past experiences with auditions, teachers, and lessons. These are usually helpful for your students. What isn't helpful is sharing things like money troubles, relationship issues, or personal grievances of any kind. If your student feels like you already have too much on your plate, they'll be less likely to come to you with questions about what they're studying with you.
Sometimes this will be a tricky road to navigate, especially with older students. I've found that being proactive about what's going to happen in any given lesson heads off any uncomfortable interactions; if there's no downtime, there's simply no time to start discussing your personal lives. If you need to write out lesson plans to keep yourself on track, so be it. I did that for the first couple years that I taught private lessons and it was immensely helpful.
On the off chance that one of my students does ask me a question about how things are going, I always answer with something positive. This is usually true, but even when it's stretching the truth, it doesn't really matter. My students pay me for my time and expertise, and it would be a misuse of the time they've paid for to spend it venting about whatever challenge I might be facing.
Being true to yourself, your personality, and your teaching style while maintaining a healthy distance between your students and your personal life isn't an easy balance to attain. When you first start teaching, you'll probably slip up. Either you'll find yourself sharing a little too much and not covering the lesson material you want to discuss, or you'll put up too much of a wall and make your students feel like you're disengaged.
These are normal mistakes.
As long as you learn from them and do your best not to repeat them, you're still a good teacher.