Referring to professors by their first names, when giving a talk,
Some professors are comfortable having students call them by their first names. You should wait until individual professors let you know that this is acceptable to them before you do so.
However, others are not comfortable with this. So, to be on the safe side, I believe that it is best to refer to them by their formal title and last name during a public talk. Many professors do this with their peers during public talks, even if members of the audience are their good colleagues. Plus, you won't run the risk of mistakenly refer to some professors by their first name and others by their formal name, which could be viewed as disrespectful.
I also caution to graduate students that even when they feel comfortable calling individual professors by their first name, they should refer to the same professor by their formal name when talking to others. It's usually best to err on the side of greater professionalism.
If you are referring to them rather than addressing them, I think you should say Firstname Lastname i.e. omit the title and say both names.
That is more natural than the alternatives, politer to the professor than just Firstname, and politer to the audience as it makes it very clear who you are referring to. It is polite whether or not you know the professor, and whether or not they are comfortable with being addressed by their first name.
Occasionally speakers refer to other researchers by nicknames such as Bob or Sasha, which don't even start with the same letters as the full first name. That makes it especially difficult for the audience to work out who they are talking about. Most people don't know all the standard nicknames in the world.
Here is what I believe to be the standard conventions in math in the US when referring to another researcher in a talk:
You write their full last name on the board (unless they're a collaborator and you've already written their name out and then an initial only may be fine).
If the person is not in the audience, then you say their last name only with no title. Or firstname lastname if they're on the job market.
If the person is in the audience you may instead refer to them as you would ordinarily (typically this means by first name or nickname, but in some situations this could mean using a title) and you look at them as you do so. You still write the last name on the board.