SOLR autocomplete for multiple terms phrase - solr

Question

I've a question re autocomplete in Solr - say there is a multi words string "nice cheap laptop" which should be suggested to users in case they type 'nice', 'cheap' or 'laptop'. How to achieve that with Solr?
I'm trying to migrate to SOLR a code that currently works with ElasticSearch - for ES the mapping is provided with type 'completion', for which I configure all permutations of the terms in the phrase as input to search against, and output is the original phrase. Couldn't find in the docs if/how this is possible with SOLR.
EDIT:
I tried adding the following to solrconfig.xml:
<searchComponent name="suggest" class="solr.SuggestComponent">
<lst name="suggester">
<str name="name">mySuggester</str>
<str name="lookupImpl">FuzzyLookupFactory</str>
<str name="dictionaryImpl">DocumentDictionaryFactory</str>
<str name="field">name</str>
<!--str name="weightField">price</str-->
<str name="suggestAnalyzerFieldType">string</str>
<str name="buildOnStartup">false</str>
</lst>
</searchComponent>
<requestHandler name="/suggest" class="solr.SearchHandler"
startup="lazy" >
<lst name="defaults">
<str name="suggest.dictionary">mySuggester</str>
<str name="suggest">true</str>
<str name="suggest.count">10</str>
</lst>
<arr name="components">
<str>suggest</str>
</arr>
</requestHandler>
And the following to managed schema:
<field name="productNameId" type="string" indexed="true" stored="true"/>
<field name="aspectId" type="pint" indexed="true" stored="true"/>
<field name="name" type="text_general" indexed="true" stored="true"/>
<field name="categoryId" type="string" indexed="true" stored="true"/>
Then indexed 3 documents with solrj:
String urlString = "http://localhost:8983/solr/aspects";
HttpSolrClient client = new HttpSolrClient.Builder(urlString).build();
client.setParser(new XMLResponseParser() );
ProductAspects pa1 = new ProductAspects();
pa1.setId("1");
pa1.setAspectId(1);
pa1.setName("alice");
ProductAspects pa2 = new ProductAspects();
pa2.setId("2");
pa2.setAspectId(2);
pa2.setName("alza");
ProductAspects pa3 = new ProductAspects();
pa3.setId("3");
pa3.setAspectId(3);
pa3.setName("alza bob");
final UpdateResponse res1 = client.addBean( pa1 );
final UpdateResponse res2 = client.addBean( pa2 );
final UpdateResponse res3 = client.addBean( pa3 );
UpdateResponse res = client.commit();
After that, I would expect that typing 'alz' would return just 2 docs, but it returns all 3 docs:
http://localhost:8983/solr/aspects/suggest?suggest.dictionary=mySuggester&suggest=true&suggest.build=true&suggest.q=alz
Can you please assist what is the correct config for autocomplete with Solr?