How do I change the Distance between notes?

Add stretch to the measure. Yes, the overall layout will be affected, but you can't make an omelette without breaking the eggs. ;o)

You could add a "hard" space (Ctrl/space) into your lyrics and you'll end up with the attached.

Not sure which "note distance" you tried; thre is no such setting, exactly. Maybe you mean "minimum note distance" in Style / General / Measure? That definitely works, but you have to turn it up high enough to matter. And it would affect all notes. For for instance, setting minimum note distance to 2sp creates lots of unnecessary extra space everywhere. But increasing it to just 0.5sp increases it by just enough to allow the hyphen to appear between "wel" and "come".

Actually, the default amount of space between "be" and "wel" looks correct to me, not sure why you'd want to increase it. More useful would be to increase the space between "wel" and "come", so there is room for the hyphen. i wouldn't mess with this until you were done entering the music, as very likely in the actual score, the spacing would be different and the additional space wouldn't be needed. But the global change I mentioned above would work. Or, if you couldn't afford the slight increase in spacing elsewhere, just click the note you to add space before and then increase the "Leading space" in the "Segment" section of the Inspector. That's if you want *all* notes at this time position to move, which you probably do so they stay aligned. If you want to mnove this one note out of position with respect to others at the same time, use the "Horizontal offset" in the "Chord" section.

Go to format/style/measure then increase the measure width

Hi Elwin
I understand you want to increase the distance between these notes so that the lyrics are more readable.
If that's what you want, you just need to select the syllable and change its centering with respect to the note.
That's what it looks like:

This worked for me: