Many people spell it wrong, because some Löwens simply dropped the umlaut on the "o" and became Lowens. However, some Löwens decided to convert the ö to oe which is it's closest pronunciation in English.
Let's take a look at the popularity of Löwen vs. Loewen in German books. Note the scale.
This Ngram chart tracks the incidence of the name "Löwen" in German books.
We can see the name Löwen is fairly popular throughout the 19th century, becoming less popular around 1880 but jumping in prevalence in 1940 before dropping to it's lowest use, while still remaining fairly well-used.
Next let's take a look at the alternate spelling "Loewen":
The most striking difference to me is the much lower incidence of the spelling Loewen in German. Which makes sense, as Loewen is an Anglicized spelling of Löwen. What is also striking is the relative evenness of its use, as there is no marked decrease in use.
Now let's take a look at English books. The percentages are much smaller here, most likely due to the fact that most Löwen's stayed in Europe and only a very few came to the new world and were mentioned in print. What is most noticeable here is the complete obscurity of the name Löwen in English until around 1900, when you start to find it mentioned in books.
What is noticeable here? A striking similarity to the shape of previous graph, showing that the name Loewen was completely unknown in English until 1860, and very obscure until a sharp rise in popularity around 1980.
Also interesting is that in the year 2000, the name Loewen is just under a hundred-thousandth of a percentage of all words in English books, whereas Löwen is around 2 millionths of a percentage of all words. As you can see, Loewen is much more popular in English than Löwen.
Ngram graphs are provided by Google.