Add a script editor web part to your view and add the following code. Adjust for column names:

<script type="text/javascript">
(function () { 
    var bodyFieldContext = {}; 
    bodyFieldContext.OnPreRender = preRender;    
    SPClientTemplates.TemplateManager.RegisterTemplateOverrides(bodyFieldContext); 
})(); 

function preRender(ctx) {   
    var userName = _spPageContextInfo.userDisplayName;
    console.log(userName);     
    var rows = ctx.ListData.Row;     
    for (var i = rows.length - 1; i >= 0; i--) {
        if ((rows[i].Field1Text != userName) && (rows[i].Field2Text != userName) && (rows[i].Field3Text != userName)) {
            rows.splice(i, 1);
        }
    }
}
</script>

This function will run before the ListViewWebPart is rendered and modify the rows. Any rows that do not match the users display name will be removed.

Add a script editor web part to your view and add the following code. Adjust for column names:

<script type="text/javascript">
(function () { 
    var bodyFieldContext = {}; 
    bodyFieldContext.OnPreRender = preRender;    
    SPClientTemplates.TemplateManager.RegisterTemplateOverrides(bodyFieldContext); 
})(); 

function preRender(ctx) {   
    var userName = _spPageContextInfo.userDisplayName;
    console.log(userName);     
    var rows = ctx.ListData.Row;     
    for (var i = rows.length - 1; i >= 0; i--) {
        if ((rows[i].Field1Text != userName) && (rows[i].Field2Text != userName) && (rows[i].Field3Text != userName)) {
            rows.splice(i, 1);
        }
    }
}
</script>

This function will run before the ListViewWebPart is rendered and modify the rows. Any rows that do not match the users display name will be removed.

All items:

With filter: