That is hard to put into actual numbers. What is clear is that this has happened. But it seems that Rhineland Poles, in the most Western part of Prussia – were subject to such practices on a much bigger scale – which might still be relatively small for the more radical changes – than those in genuinely former Polish territory now under Prussian control during the Empire, or in the case of Silesia, or some other parts of Prussia, German lands with an influx of Polish migrants.
We see some clerical errors in transcribing or transliterating Polish names, together with intentional changes, often substituting just a few characters, not existing in German Latin alphabet (like 'Ł'); exchanging y for i; using a sound approximation, a translation, or something 'new', often just vaguely related to any pre-existing alleged 'meaning'.
What we do have are applications from below: Polish speaking residents to have their names changed, and even applications or later even changes made on German names of German people that just sounded 'too Slavic' for their own tastes. And policy from above: official instructions to encourage such practices.
The intention was not to integrate the immigrants, but to "Germanize" them. In 1901, for example, the Minister of the Interior of the German Reich instructed the district president in Münster to proceed generously with the Germanization of Polish names, because name changes "are likely to promote the merging of the Polish element with the German one.
That's why today you often have to look closely to recognize Polish names in telephone directories: Piechas were probably once called Piechaczyk, Giesbergs may have been Gizelski, and Janfelds may have been Janowskis. Schimanski, too, was once a Szymański. Where Rybarczyk became Reiber, Pawlowski Paulsen or even Majrczak Mayer, the traces are blurred.
— Helmut Vensky: "Schimanskis Väter", Zeit, 2. March 2010.
Note that while 'Germanization' was in effect a programme flanked with laws and force, the family name changes when intentional were apparently 'encouraged', not forced.
June 27, 1901 "The Minister of the Interior of the German Reich instructs the District President in Münster to proceed generously with the Germanization of Polish names. He hopes that "name changes of the kind envisaged, which are likely to promote the fusion of the Polish element with the German, will receive every support and facilitation from the authorities…" Although no exact figures can be determined, at least 30,000 applications for the Germanization of Slavic names in the Ruhr area can be traced for the period from 1880 to 1935. The German government is interested in "Germanization" and integration of immigrants from Poland and Masuria.
The prejudice of the German population against anything supposedly "Polish" also causes German immigrants from the Prussian eastern provinces to discard "Slavic" sounding names. The name change was supposed to help prevent difficulties with authorities and discrimination against children at school. It is not uncommon for bearers of Polish names to choose common German surnames such as Müller, Meier or Schulze. Since these names are not very suitable for identification, the authorities are instructed to work towards name changes of a different kind. Thus, around the turn of the century, phonetically simplified family names emerge whose Slavic origin is still recognizable:
Majcrzak becomes Mayer; Gresch instead of Grzesch; Maischach instead of Majchrzak; Pizolka instead of Piszolka; Friedetzki instead of Frydecki; Piecha instead of Piechaczyk. New formations with the endings -feld or -berg are widespread: for example, Gizelski becomes Giesberg and Janowski becomes Janfeld.
Some new surnames are supposed to be translations of a Slavic name, according to the applicants: Florczak to Floren (from the given name Florian); Pawlowski to Paulsen; Prusinowski to Preußmann; Rybarczyk to Reiber." (Source: Chronik des Ruhrgebiets, WAZ book, Chronik-Verlag in der Hardenberg Kommunikation Verlags- und Mediengesellschaft mbH & Co. KG, Dortmund 1987)
Wichrowsky becomes Wichmann
My paternal ancestors also come from Poland, from the area around Posen (today: Poznań). Even today, relatives of our family still live there. In the time of industrialization in the 19th century, my ancestors came here to the Ruhr area. My grandfather Thomas, born in Bochum in 1883, was initially called Wichrowsky. Under Kaiser Wilhelm, he too took the opportunity to have his family name "Germanized". The "Polish Wichrowsky" became the "German Wichmann.
— Klaus Wichmann: "Neue Namen für polnische Arbeitsmigranten: Aus Majcrzak wird Mayer", Mühlheim-an-der-Ruhr.de, 2009
Remarkably, this letter from the Minister of the Interior is used as a source to be examined in school textbooks about European history in the context of work migration of Poles into the Rhineland. ("Europa. Unsere Geschichte", Vol 3, cap 3.5, src "Q3" PDF of sample, sadly without that actual letter)
And yet, a study published in 2000 emphasises:
The research into name changes is still in its infancy. At this point, therefore, we can only draw attention to the phenomenon of name changing, which is hardly known outside the Ruhr area, and provide an impetus for working on the topic.
— Heinz H. Menge: "Namensänderungen slawischer Familiennamen im Ruhrgebiet", in: Jürgen Macha & Gunther Müller: "Niederdeutsches Wort. Beiträge zur niederdeutschen Philologie", Vol 40, Aschendorf: Münster, 2000. (p124)