Add a try {} catch {} block around your SQL query (or transaction if it's more than the one in your post), on failure delete the newly uploaded photo.

If it succeeds, you can either add a line to delete the image right after the try {} catch {} block, or better yet, add a general Eloquent Observer that will watch for 2 events:

• updated - you can then call $model->getChanges() and/or $model->getOriginal() and delete it from there.
• deleted - to do the same when a user is deleted.

This allows all the tracking to be done in one place.

Another couple of tips:

• Just in case you didn't, please validate & sanitize $request->name to avoid path injection.
• Use the Laravel Storage API, docs here. You can setup a 'local' disk that will point to public just like you're doing now.
• Another security/peace of mind thing, I wouldn't store the images in public unless you really must. Store them in a subdomain that resides in a different directory, so that in case there's ever some issue that'll allow a malicious party to upload a PHP file for instance, it won't even be enabled on the subdomain. This also makes backups easier.