I’m not a big fan of people taking images that aren’t theirs and using them as profile images. As an artist, I know the basics of copyrights, and it’s not good to take an image that doesn’t belong to you and use it however you please. (I drew my own profile.) I’m personally cool with people using my art, as long as it’s not making money and they credit me.
I go on the internet under the name “Luna Rose” for safety purposes. Online, I am open about my disabilities, and this could make me less likely to be hired for a job if I used my real name. There’s also the issue of stalking, which women are particularly vulnerable to, and is why doxxing is a big deal.
Most likely, people who take something from Google Images are doing so because they like the picture, and they feel that it represents them in some capacity. (For example, this is why many people use random anime pics as avatars, or Rainbow Dash pictures, etc.) For example, they might have a picture of a whale because they like whales, not because they want others to think that they are a whale.
They aren’t necessarily trying to make you believe that they are the exact person in the image. Instead, the image speaks to them, so they use it. (In my opinion, they should get permission from the owner first and link back. But there’s not much I can do about it.)
If someone is feeding false information in an attempt to deceive someone, e.g. trick them into revealing personal information, then this is a serious problem. Otherwise, it’s people disregarding copyrights and/or good manners towards artists.
If you’re wondering what to do, try asking “Could you tell me about your profile picture? I’m curious.” This should give you a clear answer.
I don’t know laws about trying to pass off someone else’s image as their own, so I can’t speak to that. If the person readily admits that they did not create the image, or that they’re the one who posted the original image (e.g. I am the same artist who posted my profile picture on deviantART), then this may answer your question.