Is there a name for fried evaporated milk?
It sounds kinda similar to dulce de leche, but that is usually made with extra sweeteners added to the milk as it is cooked down.

You might look at baked milk, which is a Russian food, although it looks like the cooking down is usually less than you describe - that is, it may produce a brown crust, but the bulk of the milk is perhaps still creamy in color.

You could look at cajeta or basundi, which are made by cooking milk down into a evaporated, caramelized brown sauce.  It looks like both are usually sweetened during or after cooking, but since the sugar is added later in the process, with other flavorings to taste, I see no reason that sweetening might not equally be omitted if the flavor is enough for whoever is making it.

An interesting sort of match comes from brunost, which was made by cooking down whey into a brown sauce (Norwegian prim and Swedish messmör are variations of this) - but more recently cream and sometimes milk was added to the whey for a fattier end product.  I could see someone cutting out half the process by making something similar with only milk, instead of some balance of whey plus cream.  As a bonus, I don't believe these products usually have added sweetener, so that might be a closer match.

Honestly, there are a lot more variants where there is sugar or other sweeteners added to the milk while it cooks down and caramelizes, or even afterwards to taste, then variations where the milk is cooked down plain.  However, there's no reason why someone might not have adapted one of those recipes to omit the extra sugar for various reasons, so go ahead and figure out which name (or tradition) seems most in line with what your friend makes.