You are not going to get actively "penalized" for such a trivial offence (I'm assuming you're not stuffing the ALT attribute with reams of text).
Incorrectly assigned ALT text is a common faux pas.
However, this isn't going to do you any favours either and your site is going to be less "accessible" as a result.
Is it good practice to include page name in alt tag?
"Good practice" doesn't really enter into it. (But, no, it's not "good practice".)
The ALT text is meant to be alternative text for the image - when the image cannot be used (for whatever reason). Does the "page name" relate directly to the image content (probably not)?
If you are unable to supply meaningful ALT text, then it is probably best to provide no ALT text at all. ie. an empty ALT attribute. (At least then you won't frustrate your users quite so much.)