I feel that this question is relevant in this thread - What would have to happen for you to believe that you were mad? How bizarre or mundane may a thing be before you assume that it is your apparatus that is at fault?
I remember one of my neighbours making a joke about how they didn't intend to get married because they already had 3 voices in their head and didn't need 4 ;P
I should imagine that with madness, it depends first on what madness it is - then on to what degree, then finally on how it is treated.
Regarding the first and second, if you started hearing/seeing things, going into panic attacks, depressive swings, manic excitement or any number of impairments or unusual behaviour, you might not be too concerned if it was all to a temporary degree, i.e. the result of extreme temporary environmental stress or poisoning by some psychoactive substance. I think we've all had at least one moment in our lives when we've been awake for 2-3 days and had the moment of realisation that we need to sleep or shall surely die, with the accompanied loss of mental coherence. Yet we would not be too concerned with such an episode because the cause, effect and cure are all known, and it is known that such effects are temporary.
If however the mental illness is not temporary, its cause is not known nor is its cure known, then it would be more concerning - but you would also need a frame of reference to know that you were mad. If you lived your whole life with auditory hallucinations, you would not be aware this is abnormal without discussing it with doctors, or having lived a life without the auditory hallucinations. I also think most people would not think of themselves as mad until such time as the madness became debilitating, much in the same way that people with depression will most likely tell you everything is fine
The last thing is obviously how it is treated, with special note to how stigmatised mental illness is wherever you are. I don't think Lovecraft's hereditary madness stories would be as punishing if mental healthcare back then wasn't a horror in its own right, nor the stigma of mental illness so potent. I imagine that a Lovecraft story set in a competent Britain would end as such:
Protagonist: 'Doctor I'm hearing and seeing things after moving into my family's ancestral halls.'
GP: 'I'll send you to a mental health specialist then if it's cool with you.'
Protagonist: 'Cool b'
Protagonist is referred to psychiatristPsychiatrist: 'What's wrong?'
Protagonist: 'I'm hearing rats in the walls but the vermin exterminators found nothing. Pretty certain I'm hearing things,'
Psychiatrist: 'Do you have a family history of any mental health, illnesses, work stress, drug use, anything you might suspect?'
Protagonist: 'Yeah lol centuries of madness, auditory hallucinations, psychotic episodes, orgies & serial killings. Also I'm pretty stressed out after moving here from America since I'm friends with basically no one here and I'm living all alone with my cat.'
Psychiatrist: 'Hmmm yeah dude that sounds like it might be important information, anything else? I aint judging, this is a safe space'
Protagonist: 'I feel like I'm pursued by a curse on the De la Poe family, like my destiny is out of my hands, that I'm always watched and my family house is built upon ancient cursed ruins. Also my friends are saying I've changed, since I've given up everything to pursue my family history with an interest they say is obsessive - I think they're up to something, just like those villagers who judge me behind my back.'
Psychiatrist: 'Yeah sounds like it could be early signs of schizophrenia, which can manifest symptoms of paranoia, auditory hallucinations and acute behavioural changes. You living in your family house still?'
Protagonist: 'Shit's pretty spooky. Big castle full of gargoyles and accursed, thrice-damned villagers, who call me a monster.'
Psychiatrist: 'Tell you what, find somewhere nicer to stay because the stress and significance of the house to you personally might be exacerbating your condition, while the community sounds pretty unwelcoming. I'll refer you to a community mental health team while we run some diagnostic tests to try and determine the cause of your condition, we don't want to rule out anything just yet.'
Protagonist: 'Sounds cool fam, I wouldn't want to eat my best friend's face off while screaming about De la Poes doing as De la Poes have done'
Psychiatrist: 'Yeah we want to avoid that kinda stuff'