You can do a left outer join on the tables (under the Links tab of the Database Expert). This way, all the fields from the leftmost table are selected even if there isn't a match with a field in the right most table.

Yep, there is always PLENTY to learn about Crystal Reports. In fact, if you check out my Encyclopedia book, you'll have more than enough information to keep you busy learning all of its features. 

When you do an outer join, any fields from the table that doesn't have a matching record are simply NULL.  So, the simple solution is to check for NULL values, and replace them with "OTHER."  This can be done through a formula, possibly through a Top N grouping (depending on your data and what you want to show), or by defining a default value and having Crystal show the default instead of NULL.

Now, if you want Crystal to know that, if Mary doesn't have any records in Table B, and there are records in Table B that don't have a name, then those records belong to Mary....  Well, that's a lot trickier.  In a single case, it's relatively easy.  Check for NULLs on each side, and match them up.  But, what happens if there are two names that don't have matching records?  How do you sort out which ones go where?  In that case, I think your efforts would honestly be better spent cleaning up your data before it ever reaches Crystal.  Because, while I imagine it could be done, it's going to be a tough row to hoe.

I think the simplest solution would be to create a formula that tested for NULLs.

IF ISNULL({MyReport.AName}) OR ISNULL({MyReport.BName}) THEN
    "Other"
Else
    {MyReport.AName}

Then simply group on this formula.  This will, I think, give you the results you want.  You can additionally create another group on AName that will help sort out the results under "Other" if you'd like.