Try with the following field type for your field(complete_name) in schema.xml,
<fieldType name="text_search" class="solr.TextField" sortMissingLast="true" omitNorms="true">
<analyzer>
<tokenizer class="solr.KeywordTokenizerFactory"/>
<filter class="solr.LowerCaseFilterFactory" />
</analyzer>
</fieldType>
and your field definition in schema.xml is like
<field name="complete_name" type="text_search" indexed="true" stored="true"/>
and search with the query like
q=complete_name:*Joseph\ Gar*
To handle special characters other than alphabets and numbers, use the escape character \ on before every character. Example: To search for text contains $, give q=*\$*
Hope this answer may resolve your problem.