<apex:repeat var="list" value="{!tesList}">
        <input type="checkbox" style="display:{!IF(CONTAINS(anotherList, list['name']), '','none')}" value="{!list['name']}" />
    </apex:repeat>

<!-- JSTL sample -->
    <c:forEach var="list" items="${testList}">
            <c:if test="${fn:contains(anotherList, list.name)}">
                <input type="checkbox"  value="${list.name}" />
            </c:if>
    </c:forEach>

testList = new List<String>{'NAME_A','NAME_B','NAME_C'};

<!-- The following output works good as if it where a string -->
testList: {!testList}

<apex:variable var="list" value="{!''}{!testList}" />

NAME_A: {!IF(CONTAINS(list, 'NAME_A'),'OK','FALSE')} <br/>
BLAAHH: {!IF(CONTAINS(list, 'BLAAHH'),'OK','FALSE')}

NAME_A: OK
BLAAHH: FALSE

<apex:variable var="list" value="{!''}{!anotherList}" />

<apex:repeat var="list" value="{!tesList}">
    <input type="checkbox" style="display:{!IF(CONTAINS(anotherList, list['name']), '','none')}" value="{!list['name']}" />
</apex:repeat>