When you join a new team in a new organization, do everyone a favor and kill the old organization as quickly as you can. Every reference and example to your former team and organization is the sound of a jackhammer to your new colleagues.
“At ABC we did this…” “At ABC did that…” “When I was at ABC, we learned that…”
It will only take a week or so of this kind of yammering and your new colleagues will likely be asking themselves, “If the old organization was so great, why did you leave to come here?” They will be ready to chip in and pay for a one-way ticket back for you.
Eliminating any and all references to your former place of employment doesn’t mean you have to jettison your knowledge, as well. You simply need to omit the reference. Instead of saying, “At ABC, we used a process that worked great…,” think about saying, “I know a process that works really well to address this challenge.”
The sooner you dispatch the old team and organization, the better. You’ve already moved. So, move on.