I think you want:

$params = array(
    'type' => 'group',
    'limit' => 0,
    'metadata_name_value_pairs' => array('name' => 'universal_categories', 'value' => '%'.$query.'%', 'operand' => 'LIKE')
);

(setting the limit to 0 means no limit).

Ah, sorry. I missed the point that this value is in the group name.

Group names are not metadata.

Instead I think that you could code this as:

$params = array(
    'type => 'group',
    'wheres' => array("e.name LIKE '%$query%'"),
    'limit' => 0,
);
$objects = elgg_get_entities($params);

It doesn't work:
Unknown column 'e.name' in 'where clause'

The query:
SELECT DISTINCT e.* FROM elgg_entities e WHERE e.name LIKE '%espiritualidad%' AND ((e.type = 'group')) AND (e.site_guid IN (1)) AND ( (1 = 1) and e.enabled='yes') ORDER BY e.time_created desc

The table elgg_entities don't have the colum "name". :-/

You need to do a join on a groups table, and use g.name

Ismayil is right, that should have been:

$params = array(
    'type => 'group',  
    'joins' = array("INNER JOIN groups g ON (g.guid = e.guid)"),
    'wheres' => array("g.name LIKE '%$query%'"),
    'limit' => 0,
);
$objects = elgg_get_entities($params);

Bit of a wart in the API that you need to do the little dance for certain values that aren't metadata.

I believe elgg_get_entities_from_attributes() is coming with 1.9, that will make life easier.

Thanks, it works perfectly!!

I somewhat new to Elgg, but I'm having the same issue.  If you search on only part of a group name, we want all of the groups that match to be returned, but zero results are coming back.  I generally understand what the code above is doing, but I'm not clear about where it needs to go.  Any pointers would be appreciated greatly.  Thanks.