Well, yes, but that's because there is insufficient room to fit your current layout into 500px.
A min-width of 640px will prevent the menu going under the name (although to be honest I don't see this as a big issue). You can probably get away with a smaller min-width by reducing the padding on your menu items.
You might also want to look into using @media queries
to make your layout responsive - this would allow you (for example) to space your menu items less on a smaller screen.