I think this is possible, but it will require some fairly custom logic on your end. HubDB doesn't support OR logic in filtering, which is what you're trying to do here. You're basically trying to grab words from an input and match them against either a first name field OR a last name field.
But without using a filter on the table, we can still create some custom logic for this.
{% set names = request.query_dict.name|split(" ") %}
{% set table = hubdb_table_rows(XXXX) %}
{% for row in table %}
{% for name in names %}
{# print out table cells that you need when names match table cell values #}
{% endfor %} {# end for name in names #}
{% endfor %} {# end for row in table #}
It's not exactly the same thing because you're actually pulling the entire table. But I think this would enable you to accomplish what you're going for. Let me know if that makes sense or if you have any questions about setting it up.