Girls, My boyfriend saved his ex lovers number under a fake name?

Hi I am christell. Me and my boyfriend have been dating for almost a year and a half. We moved in together and we got a baby together. We have a great relationship and he is much older than me. I am a stay at home mom but not for long. I have recently started getting suspicious of him. He has been going out lately even when the baby was born he would leave us alone at home. I have found condoms in his car but he denies its his. He's been chatting with a girl from his past and even saved her number under a fake name. I confronted him but he says its nothing. I don't know if I should believe him. I need advice. Help!
Girls, My boyfriend saved his ex lovers number under a fake name?
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