Is it appropriate to say something like 'having spoken to future trainees at x firm' but not name the future trainees in your application? Alternatively I could name them, but I'm not sure if its as relevant as they aren't actually working at the firm yet. Or is it not worth talking about future trainees at all?
I think it's generally better to give names, as from the recruiter's perspective this is evidence you have actually interacted with the firm and that you have also taken care to remember the people you have spoken to. However, I do agree with
@Amma Usman's point that in the case of future trainees, you should firstly ask for their permission before naming them in an application. I would argue this is a general rule for interactions you have with people outside the setting of a career event organised by the firm - where the very purpose of all your interactions is to inform you for a potential application.
Regarding your second question about relevance, I once again agree with
@Amma Usman's response that it is fine to mention a future trainee as long as the information you learnt from them is not something you could have easily gotten from their website. The one caveat I will add is that I do not think the information given to you from a future trainee necessarily needs to be completely new to you. I believe it would be fine to mention the interaction with a future trainee if speaking to them either (i) gave you a new perspective about a feature of the firm you already knew about, or if (ii) it simply offered confirmation from practical experience about a selling point of the firm.
For instance, say you spoke to a future trainee at firm you knew had a great reputation for private equity work. You might have known this already, or could have found about it by researching online. However, say the future trainee does not stop at mentioning just this fact. Perhaps in a vacation scheme, they got to meet and speak with some of the firm's practitioners and realised that the firm's reputation attracts the best in the field, which turned out to be an unparalleled learning experience for the future trainee, which led to them accepting the TC offer. This is a new perspective on the relevance of the firm's reputation, which you could mention you learned from the person you spoke to, even if the firm's reputation is something you knew about before. Alternatively, imagine a firm heavily advertises having a very collegiate culture. A future trainee could again mention some anecdotes from their experience with the firm: how helpful people where when they reached out to them, how the recruitment team was very friendly throughout the process, how the partners were down to earth and approachable etc. While you might have know the firm advertises this collegiate culture, the conversation with a future trainee provide you with concrete evidence to this effect and is therefore relevant in an application.