Suppose that two companies have registered trademarks for the same name (somewhat different industries). Company A owns a domain with the same name as his registered trademark. Company B registered his trademark on a date earilier than Company A and now wants to own Company A's domain. Can he force A to give it up?

Can, yes. Will, maybe, maybe not. :D

I'm not a lawyer, but I'll share what I know based on what I've
learned from one who works on this field (and still learning).

It's not clear-cut as to who will retain the name due to certain
factors. At the very least, they are:

1. If the 2 companies are in related or totally different fields.
2. How company A is using the domain name.
3. What content is attached to the domain name.
4. If it reaches the UDRP, who'll convince the panelist of whose
case.

There are actually more involved.

You're asking in anticipation of it happening to you, aren't you?

Ron.
In the described scenario, are you A or B? Just curious.

I doubt it's doable since they're in different industries and there's no "bad intent".

I am curious to know what is meant by bad intent? I think you mean "bad faith" as they seem to be calling it in the domain dispute biz. Is bad faith infringement while using it in commerce? Or, does it mean cybersquating?

Basically that's it. The most challenging part is to determine and
prove the bad faith or bad intent factor...if it reaches that point.

However, in the UDRP, the first part about whether the name will
infringe on the Complainant's trademark will render the other 2
moot if the Complainant is unsuccessful in proving its case in that
aspect. In this case, there's no way Company A is infringing on
Company B's trademark since they have one of their own in a
different field (though I wonder what you meant by "somewhat" :D ).

I could be wrong, though, so it's best to seek legal advice on this,
especially one well-versed in this field.

There is something called Co-Existance where 2 trademarks exist but serve different interests. You will need to speak to a lawyer and have papers drawn up so neither party infringes on the other.