I went through this with my daughter

Ask at a good deli about dairy free cheese…. here in Aus you can get Kolios and a dairy free fetta… both are yummy. There is also a cheese called minichol that is often advertised as Dairy free but it actually doe contain dairy.

You can get soy milk (obviously), soy icecream and tofutti (which is like a dairy free cream cheese. I think it is Tofu based)

Semase seeds are a great source of calcium but the calcium is not well absorbed unless the seeds are ground. So you can add a small handful of ground sesame seeds to some cereal to help your calcium intake.

As for different names for dairy. Avoid anything that contains:
Milk, milk solids (full fat or skim), butter, cream.

There is also an emulsifier that contains dairy but I can’t remember which one it is…I never had a problem with it though, and my sister is quite badly dairy intolerant and she can eat the emulsifier too with no probs.

Oh and Nuttelex (a butter type spead which is a great alternative on toast/sandwhiches and in cooking/baking)

Hope that helps, let me know if you have any other questions