Is this signature real?

Possibly, but that is such a bad photo that it is hard to tell.

Do you have a better picture and information on where the signature is from, a note, letter, book, etc.

I mean, it is a horribly compressed (low resolution) image, but I don't see anything alarming from what is visible.

It's hard to tell with such a grainy image, do you have a better one?

What provenance do you have?

Came across that image on a site and thought l would ask here since l saw you guy's video on your yt channel about it (great stuff on there btw!) But, l did have this one saved from quite a while back when this book was out for sale. As you can see on this one it's from a swedish edition, the first hardback, which makes it a bit alarming (l guess you're familiar with the story about that translation). But perhaps our professor hadn't had had any time to look at it at the time of this signing? How likely is that?
l can say that the second name does seem swedish with perhaps german roots.

Thanks for the additional context.

Tolkien had read (and disliked) the Swedish translation circa 1957, so a long time before this image is dated. I don't think Tolkien disliked it so much that he would refuse to sign a copy if presented one by a Swedish fan, though.

There's no certainty, but again with the better quality image the handwriting looks ok to me in the picture.

Agreed, this looks correct.