Can he be lying or telling the truth?

So last night me & my bf were at a family party and he was on his phone I snooped up from behind & I saw his snapchat & some girls name popped up which I recognized . I told him who was that & he told me it was his friend . I didn't believe him . & I told him are you lying ? Only because his mom told me about his ex gf & I found out her name . & the name I saw. On snapchat was her name . & his mom showed me a picture of her. He told me why would I have you move in , most likely put a finger on it & have a child with you . He said you think I would do something like that & stil consider doing all these things with you? & I didn't know wether to believe him or not. & he explained to me how the girl looked & I t was a different girl  but still I have a right to be mad right ? I feel like I can't trust him with social media at all . Anybody think this is something I need to worry about. ? About the girl ? Even if it's not her ? He wants me to move in and wants to eventually get married and have kids one day but how can we move pass forward if I find stuff like this ? & I think bad? He tells me I'm the only one for him