Boyfriend lying?

Hey, so my boyfriend and I have been dating for 9 months & we’re doing great, had a lot of ups and down and trails and all but we always make it out and become stronger together. He has lied in the past and it was very difficult time but with time and trust I’m becoming more trusting of him . There’s just one thing I’m unsure of.

He is on medication ( so he says ) for bipolar anxiety. I have NEVER seen him take the medication( we don’t live together ) but I go over his house and never saw it or anything. I asked him abt it he says he’s on it. He showed me the bottle . Annoyingenough him and his father have the same name so I was kind of suspicious about it since his dad is on many medications as well. I asked him if I can see him taking it thinking it’ll help me believe him but he feels that’s super unnecessary and that I should just trust and believe him.. should I just drop it and trust ?!