LINQ is, as the name suggests, more of a query tools. So you can get specific item(s) that you want to modify from a collection using LINQ, but the modification itself is out-of-scope for LINQ.
Assuming that there is always maximum one match to your criteria, you can do as follows :
var john = items.FirstOrDefault(o => o.tag == "{John}");
if(john != null)
{
john.value = "Jane";
}
Otherwise, you can use LINQ Where(o => o.tag == "{John}")
to get the target items for modification. But then you'll need to iterate through the result to actually update the value of each matched item.