German here.
It is indeed more like "Hime" here, and I guess "Hame" in Sweden. The word is in use in lots of city and village names, just like various other general names that indicate local landmarks.

"Berg", "Bach", "Heim", "Au", "Tal", "Feld".

In English:
"Hill", "Creek", "Home", "Shire" or "Meadow", "Valley", "Field".

In the "Pfalz", where I hail from, you will find tons of "Berg" and "Bach" villages.
Stelzenberg, Otterberg, Otterbach, Weselberg, Mölschbach, Reifenberg, Krickenbach, Schmalenberg, and so on and on.

The word means home and it's in use by various European languages. :p But in Norwegian or Icelandic it would sound more like the former I suppose.

Many thanks sir. I'm in Wisconsin (US) but my grandfather was from a small town near Vienna. My spouse and I had lunch at a local establishment run by a couple from Vienna and I asked him if he was familiar with this small town and he nearly exploded laughing at my attempt at pronouncing the name. "You should visit there, but first some language lessons perhaps?" Amen.

Also, I was watching a podcast interview with one of the Iron Gate developers and he pronounced it Val-hAme not Val-hIme. I will defer to our Scandinavian players to provide the correct English pronounciation.