currently no support exists for this feature. Could probably add some hack to extensions/Elastica/ElasticaConnection.php in the getIndexName() method to prefix with something though. I think that would cover all use cases, but would have to try it out and see that everything really does go through that method like it should.

@EBernhardson, yes it seems to work.
I defined a prefix 'wwi_' and let the function retrn $prefix . $name

Then I run CirrusSearch/maintenance
php updateSearchIndexConfig.php --startOver
php forceSearchIndex.php

Marvel plugin shows the new indexes
wwi_mw_cirrus_versions
wwi_wikidb-en __ content_first
wwi_wikidb-en __ general_first
and search works, also after I delete the previous indexes via Elasticsearch commands.

It will be easy to define such a prefix via $wgElasticaIndexPrefix

My function getIndexName reads now:
public function getIndexName( $name, $type = false, $identifier = false ) {

        global $wgElasticaIndexPrefix;  //Alois
        if ( $type ) {
                $name .= '_' . $type;
        }
        if ( $identifier ) {
                $name .= '_' . $identifier;
        }
        if ( isset($wgElasticaIndexPrefix) ) {  //Alois 3 lines
          return $wgElasticaIndexPrefix.$name;
        }
        return $name;
}

In LocalSettings.php I have
// created by Alois for extensions/Elastica/ElasticaConnection.php
$wgElasticaIndexPrefix = 'wwi_';

Glad that worked for you! I'm going to make some changes soon to allow explicitly setting per-wiki index prefixes rather than using the wiki name (although that will stay the default). That work will be attached to T140434