[ select Layout.Name from ProfileLayout where ProfileId = :UserInfo.getProfileId() AND RecordTypeId = :record.RecordTypeId ]

static String restGet(String endPoint, String method, String sid) {
    Http h = new Http();
    HttpRequest hr = new HttpRequest();
    hr.setHeader('Authorization', 'Bearer ' + sid);
    hr.setTimeout(60000);
    hr.setEndpoint(endPoint);
    hr.setMethod(method);
    HttpResponse r = h.send(hr);
    return r.getBody();
}
static String toolingAPISOQL( String query) {
    String baseURL = URL.getSalesforceBaseUrl().toExternalForm();
    return restGet( baseURL +
'/services/data/v41.0/tooling/query?q='+ (query.replace(' ', '+'))
,
'GET', UserInfo.getSessionId() );
}

static String getLayoutNameForCurrentUserProfile( Id recordId ) {
    String body = toolingAPISOQL('select Layout.Name from ProfileLayout where ProfileId = '' + UserInfo.getProfileId() + '' AND RecordTypeId = '' + [ select RecordTypeId  from Account where id = :recordId].RecordTypeId + ''');
    System.debug(LoggingLevel.ERROR, '@@@ v: ' + body );
    String name = body.substringBetween('"Name":"', '"');
    System.debug(LoggingLevel.ERROR, '@@@ v: ' + name );
    return name;
}
getLayoutNameForCurrentUserProfile('001g000001hLEAj');