Last name, First name or Last name, First name, Patronymic — during the first meeting, it's perfectly normal and necessary to ask for the full name. If you didn't catch it, don't hesitate to ask again. But if you do this on the second meeting, it will be disrespectful.
Place of work and position are essential for your client database. During a simple internet search, you can identify the basic needs of people in their professional activities. Perhaps one of them turns out to be a procurement manager in a major construction company, while you may decide to work as a metal trade manager. In other words, you may have contacts of potential clients without even realizing it. So take immediate action to bring order!
The birthday is a crucial date. It's a way to break the ice with pleasant words or with a thoughtful gift for your partner.
Professional holidays. Do you know, for example, when Lawyer's Day is? Write down that date separately and set a reminder.
During the conversation, other important details may come up, such as marital status, pets, hobbies like skiing or snowboarding, children, and much more. Your memory won't retain ALL of this information, so notes are perfect (just make sure they are synchronized via the cloud to your new devices). Based on these details, you can make various useful conclusions in the future.