Hei Síman!

I see your point here. "Sólja í Ólavsstovu" is really her full
(enough) name, and the strange thing here is the preposition "í". Of
course, any preposition like "á", "undir", "yvir" et cetera would be
as strange as "í". The question is, is a name like
[first name] + [preposition] + [geographical location]
typically Faroese?
The answer is no!
I have a wellknow example from my own neighbourhood here: "Kaj på
Höjda" - "Kaj on the Hill". He is an artist from Gåxsjö (Gauksjö) in
Jamtland, Sweden, who uses this name as a signature on his paintings.
His "real" name is "Kaj Persson", which reveals that his grandfather
probably had the name Per.
Here is a website about him:
http://www.stromsund.se/konst/kaj/juli02.htm

To have an official name like "Kaj på Höjda" is very rare where I
live, but it's not too rare to have an unofficial name like this.

Another example is a fictiuos one. "Allan i Dalen" (I think Dalen is
short for the suburbian town of Enskededalen in Stockholm) which is
known from the Swedish tv-show "Percy tårar" (Tears of Percy). Here
he sings
http://personal.inet.fi/private/tomas.karlsson/allan_i_dalen.au and
this is what he looks like
http://personal.inet.fi/private/tomas.karlsson/allan_i_dalen.JPEG
(I found these sound-files at
http://personal.inet.fi/private/tomas.karlsson/percy_tarar.html )

Conclusion:
To have an official name like "Sólja í Ólavsstovu" is rare in at
least Sweden, but instead it is not too rare as an unofficial name.

Best regards,
   Jens