No, the scripture doesn't "strongly imply" that. When it names Jesus's brothers and sisters, most of them are also named elsewhere children of another woman. We have been here before; if you want to imply something from what reading you do, that is your right, but for what the scripture does or does not say, I have better authority and they disagree with you.
Mary had children aside from Christ. Get used to it.
You are aware that there were very few Jewish names during that time. Naming them elsewhere is your supposition. It isn't Scriptural. The Bible says Jesus's brothers and sisters were coming to Him. Period.