I’ve noticed several people asking this question online.
The answer is: NO. There isn’t even a hint of confusion to anyone who has read the books, (who would know that Professor Minerva McGonagall
never married and* has no children, and that Filch’s full name is Argus Filch so they don’t have the same last name anyway, and also his magical family is ashamed of his being a squib and I don’t think McGonagall would ever be ashamed of her own child if she had one). But for people whose knowledge of the Harry Potter universe is informed only by the film adaptations, I think I can pinpoint the moment of misunderstanding.
About forty minutes into Harry Potter and the Deathly Hallows part 2, after Harry has returned to Hogwarts and Professor McGonagall has dueled Snape right out the window, and Voldemort projects his voice and says they should hand over Potter, and Pansy Parkinson yells “someone grab him!”, then Filch comes running into the Great Hall where everyone else is assembled shouting about the students being “out of bed!” An exasperated McGonagall says, “They are supposed to be out of bed, you blithering idiot!” An abashed Filch responds, “Oh…sorry Ma’am.” Next McGonagall intones, “As it happens, Filch, your arrival is most opportune. If you would I would like you please to lead Miss Parkinson and the rest of Slytherin House from the hall,” and Filch asks, “Exactly where is it I’ll be leading them to, Ma’am?” (To which McGonagall zings “The dungeons would do,” an exchange I have outlined non-linguistic criticisms for elsewhere.)
The confusion for audience members who have only watched the movies lies in Filch’s dialect; although “ma’am” rhymes with “ham” in Standard American English, in some dialects of British English is rhymes with “farm.” Furthermore in some dialects of British English “r”s are deleted, so that pronouncing “ma’am” to sound like “farm” but dropping the “r” ends up sounding like the Standard American English pronunciation for “mom.”
Okay? Got it, confused googler? Now why don’t you start actually reading the Harry Potter books instead of googling silly questions like this one? They are great reads and I promise there are a plethora of rich and interesting character relationships and dynamics, even if Filch being McGonagall’s son isn’t one of them.
*information released on Pottermore.com has now informed us that McGonagall was in fact married.