[Nexus]

Событие Keyup срабатывает при любом нажатии клавиши.

Попробуйте так:

window.addEventListener('load', function () {
    var MIN_CHARACTERS_NUMBER = 1;
    var DELAY = 300;// ms
    
    var nameInput = document.querySelector('.name_input'),
        hugeList = document.getElementById('huge_list');
        
    if (!nameInput || !hugeList) {
        return void console.error('Input or List not found');
    }
    
    var getRequestUrl = function (queryString) {
        return 'query.php?query=' + encodeURIComponent(queryString) + '&data=' + new Date();
    };
    
    var abortController,
        timer = 0;
    
    nameInput.addEventListener('input', function (event) {
        var value = this.value.trim();
        if (value.length < MIN_CHARACTERS_NUMBER) {
            return;
        }
        
        clearTimeout(timer);
        
        timer = setTimeout(function (queryString) {
            var requestUrl = getRequestUrl(queryString);
            
            if (abortController) {
                abortController.abort();
            }
            
            abortController = new AbortController();
            
            fetch(requestUrl, {
                signal: abortController.signal
            }).then(function (res) {
                return res.json();
            }).then(function (response) {
                abortController = undefined;
                
                hugeList.innerHTML = '';

                response.forEach(function (item) {
                    var listItem = document.createElement('option');
                    listItem.value = item;

                    hugeList.appendChild(listItem);
                });
            });
        }, DELAY, value);
    });
});