How to use JSON path wildcards in JSON_QUERY?
Looks like that is not currently supported, and would make a good feedback item.

You can get the names into a resultset with a query like:

select json_value(v.value,'$.Name') Name
from openjson(@json,'$.Dims') v


And from there you can construct a new JSON doc, but if you want an array of primitives, you need to do something like this. 

select concat('[',string_agg( quotename(json_value(v.value,'$.Name'), '"'), ', ')  WITHIN GROUP ( ORDER BY [key] )   ,']')
from openjson(@json,'$.Dims') v


I don't think there is a way to get an array of primitive values (ie not objects) with FOR JSON queries.