Are names like Anne, Karen, or Kenny ever used in Scotland?

Yup all pretty common (in the often used sense) esp Anne/ Annie as in Lennox for example (Singer and Neighbour of The Broons a LONG running Scottish Cartoon strip that appears in the top Scottish newpaper The Sunday Post ) and Kenny/ Ken there's the Golfer/ Golf Pundit Ken Brown. My Friend in Scotland has ghillie (Gamekeeper and hunting attendant) called Ken and he is more scottish than Nessie eating a haggis plus he looks like the man on the Scots Porage Oats Box tasty.

Thompson is English from the viking settlers (Which unsurprisingly have very strong links in Scotland) as in son of Tom it could be used all over the British Isles

Yes, they are frequently used in Scotland, as well as England, Wales, Ireland and every other English-speaking country.

The only Thompson know lives in England. He's Scottish. You need to realise just how much people move about these days.

Thompson surname: America or England

If you want it to sound definitely Scottish, I'd use Mc...something

Ian McConnell or something

Scottish people I know

Peter, Terry, Ian, Maxwell, John, Anne, Patsy, Margaret, Sheila, Heather, Elaine, Neil, Gina

But I don't know much I live in the US

Yes, I am from Scotland and I've met many people with these names. Thompson sounds Scottish.

Used in Scotland?

Anne - Yes.

Karen - Yes.

Kenny - Not really, more likely to be Kenneth.

Thompson - Anywhere, including Scotland.

Those are all common.

The best Scottish footballer is called Kenny Dalglish.

http://en.wikipedia.org/wiki/Kenny_Dalglish