Function that tests and mutates
I would call this method AcquireTimeSlot or similar, since the main action here is actually capturing a timely-limited resource. Result of the method specifies whether resource has been acquired or not. You may also call it TryAcquireTimeSlot to highlight the fact that acquisition may fail.

As a side note - you can rewrite the code without locks in case if that's the only place you use the lockObject. It will be a bit more verbose though...

public class TimeWindow
{
    private static readonly object _lockObject = new object();
    private long _timestampTicks;
    private int _windowCounter;

    private void CheckWindowExpiration(int windowSeconds)
    {
        long timestampTicks = _timestampTicks;
        while (TimeSpan.FromTicks(DateTime.Now.Ticks - timestampTicks).TotalSeconds &gt; windowSeconds)
        {
            if (Interlocked.CompareExchange(ref _timestampTicks, DateTime.Now.Ticks, timestampTicks) == timestampTicks)
            {
                _windowCounter = 0;
                break;
            }

            timestampTicks = _timestampTicks;
        }
    }

    public bool TryAcquireTimeSlot(int windowSeconds)
    {
        CheckWindowExpiration(windowSeconds);

        int windowCounter = _windowCounter;
        while (windowCounter &lt; 10)
        {
            if (Interlocked.CompareExchange(ref _windowCounter, windowCounter + 1, windowCounter) == windowCounter)
                return true;

            windowCounter = _windowCounter;
        }

        return false;
    }
}