The scan will work your dates back to the day of your last period (gestation age used on the scan is how long from the period).
Your period came on 1st June, which would give you a current gestational age of 9 weeks 6 days today. It is always a bit of a guess as we don't all ovulate on day 14 and the embryo does not always implant immediately (they say 5-10 days to implant). That means that although you would be from your period 9+6, if you ovulated later or implanted later you could be a bit less than that (which could give you the 8+6 reading).
It is all a bit more difficult at early stages because we are only talking a couple of centimetres (your little one is probably only about 2.5cm long) so a couple of millimetres out on the measurement can account to days.
For the dates you have, you have to have conceived after your period on 1st June and it has to be your boyfriend/the ex you got back together with.
For it to be from your ONS, it would date back to your period before 1st June. Was that around 1st May? You mentioned 12th May, but that would only be 2 weeks before your bleed on 1st June? If your period was around 1st May then 1st June, for it to be the ONS, your pregnancy would date back to the period on 1st May, so you would be 14 weeks and 2 day, which is quite a difference from what you are measuring and would not work.
If you did have a period on 12th May and then on 1st June, for you to get pregnant from that cycle, you would now be 12 weeks and 5 days, which is still a long way out from what you are measuring.
I think it can only be, from the details you have given, that you got pregnant from your period on 1st June by your boyfriend to be around the 9 weeks and 6 days pregnant (or a bit less if you ovulated late).
As your pregnancy goes on the due date estimate will get clearer, but as pp has said, at 9+6 you will be due around 7th March, but you may be due slightly after that if you ovulated a little later.