You can hide the "My Sites" menu from Liferay Docbar by creating hook. In my example i am hidding the menu option for all the users except those whose role is Administrator. You need to Hook the html/taglib/ui/my_sites/page.jsp

Add the following code to check whether the logged in user is administrator role.

boolean isAdminUser=permissionChecker.isOmniadmin();

Hence if the logged in user is Administrator we are showing the My Sites menu else hidding it. I added extra condition of isAdminUser in following code for same.

<c:if test="<%= !mySiteGroups.isEmpty() && isAdminUser %>">

Following is the code snippet from page.jsp

<%@ include file="/html/taglib/init.jsp" %>

<%
String[] classNames = (String[])request.getAttribute("liferay-ui:my_sites:classNames");
String cssClass = GetterUtil.getString((String)request.getAttribute("liferay-ui:my_sites:cssClass"));
boolean includeControlPanel = GetterUtil.getBoolean((String)request.getAttribute("liferay-ui:my_sites:includeControlPanel"));
int max = GetterUtil.getInteger((String)request.getAttribute("liferay-ui:my_sites:max"));

if (max <= 0) {
    max = PropsValues.MY_SITES_MAX_ELEMENTS;
}

List<Group> mySiteGroups = user.getMySiteGroups(classNames, includeControlPanel, max);
boolean isAdminUser=permissionChecker.isOmniadmin();
System.out.println("\n\n\n\n\n\n  isAdminUser \n\n\n\n\n\n"+isAdminUser);
%>

<c:if test="<%= !mySiteGroups.isEmpty() && isAdminUser %>">
    <ul class="taglib-my-sites <%= cssClass %>">

        <%
        PortletURL portletURL = new PortletURLImpl(request, PortletKeys.SITE_REDIRECTOR, plid, PortletRequest.ACTION_PHASE);

        portletURL.setParameter("struts_action", "/my_sites/view");
        portletURL.setPortletMode(PortletMode.VIEW);
        portletURL.setWindowState(WindowState.NORMAL);

        for (Group mySiteGroup : mySiteGroups) {
            String escapedSiteName = HtmlUtil.escape(mySiteGroup.getName());

            boolean showPublicSite = mySiteGroup.isShowSite(permissionChecker, false);
            boolean showPrivateSite = mySiteGroup.isShowSite(permissionChecker, true);
        %>
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