Is my wealth not in sync with my car?

Hello everyone, I have noticed this problem for quite a while now and hope to have this cleared up by getting some answers from you all.
I am a 28 years old male and my father (very wealthy), bought me a $410k house all paid off under my name when I got my first job after college. However, I never bothered changing my 2012 Corolla.
I honestly could pick up a 4-series bmw right now in cash, no payment if I choose to but I find it extremely impractical as my old car still runs perfectly fine.
People automatically assume I am not rich nor not well off because I do not have a nice car.
No one possibly imagine that I have a brand new designer style house without and mortgage or rent.

Last girl that I have dated from work, (I strictly don't bring girls to my house for the first few weeks, because I cannot trust whether they like me for wealth or love), left me before she found out that I own a very nice house despite my age. When I had co-workers over for dinner on Thanksgiving last year, she was literally in awe when she saw what kind of house I live in and she started to act differently around me at work.

Whats funny is that people in my work place have a nice car yet they still live in a small apartment, yet people seem to get more noticed/appreciated for their "social class", paying 2000 dollars a month on rent and 800 dollars a month on a car lease when they make less than 4k a month.

Should someone like me be driving a luxury car to match my house to get with the norm?

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