While using lyx, I see that it remembers my last used math command. For example, if I write \Phi, and then right after that if I begin to write \P, it will show me in the suggestion Phi so that I can just press Tab and complete it. But I would like it to remember my most used math commands in general and not just the last used one. For example, I never use \Game but I frequently use \Gamma. So, when I start writing \Ga, it won't pop-suggest \Gamma but instead, it pops with the suggestion \Game which I don't ever need. Is there a way for lyx to have just the most used math commands in it's auto-complete suggestions ?
No, LyX's math auto-completion is currently not smart enough. There is an enhancement request for what you would like here. If you would like, you should register on LyX's trac, and CC yourself in the issue, and add any comment to clarify the enhancement request. By doing that, you bring attention to the issue and it is more likely to catch an eye of a LyX developer who might decide to work on that issue. If you happen to have any C++ knowledge, patches would also be welcome.