In real life I believe it would be the same way. Humans lie and keep loads of secrets more than you think. In real life, Banri would have acted the same way.
I find it odd that you're unable to relate to this though. Would you openly tell people that you lost your memory and don't know anyone including your friends and parents? Majority of people won't because it confuses them enough already and it most likely stresses them out a lot. Mentioning it, would be difficult for them and would force them to face the truth. Banri moved to tokyo to avoid his past, many people do this in real life for less tragic situations like a breakup which affected you a lot, people will try to avoid contact and try avoid anything that reminds them of the situation.
And now that he has accepted the situation, having not told Yana and the others about his past and injury. Especially since Yana thinks he's been a good friend, Banri feels guilty that he hasn't told him about it and since he only recently found out about Yana and Linda, it's hard telling his friend that he used to be best friends with Linda and that he loved her. That could potentially ruin the relationship between Yana nad Banri. Banri doesn't want that, even though Banri doesn't mean any harm, Yana will definitely take it the wrong way.