I like to fast in the winter because the days are short. Of course I hope for the reward of Allah, but I also hope to lose a little weight. Is it permissible for me to combine two intentions? Another question also occurred to me: many people – including myself – are afraid of sin and of committing haraam actions for fear of what people will say, or for fear of scandal or shame, or loss of dignity and self-pride. Will that be good for a person in the hereafter?

Praise be to Allah

Firstly: 

There is nothing wrong with combining the intention of seeking reward for
fasting and the intention of losing weight, although it is preferable for a
person to intend his fasting for the purpose of attaining reward only.
Losing weight will inevitably happen when one fasts, whether one intends
that or not. 

As-Suyooti (may Allah have mercy on him) said in al-Ashbaah wa’n-Nazaa’ir
(pp. 21-22):

Combined intentions (and motives) are of many types. Firstly, a person may
have, alongside the intention of worship, a motive that is not worship but
will not invalidate it. One example of that is if a person intends to do
wudoo’ or ghusl, and also to cool himself. There are some views which
suggest that it is not valid because of that combined intention, but the
more correct view is that it is valid, because cooling oneself is something
that will inevitably happen, regardless of whether or not that was part of
the motive for doing wudoo’ or ghusl. So he did not plan to have a combined
intention, and he did not intend to undermine his sincerity; rather his
intention was to do an act of worship in a manner or at a time that is
prescribed, because one of its inevitable outcomes is cooling oneself. The
same applies if a person has the intention to fast, and also has another
motive, namely the desire to avoid certain foods for reasons of health. But
there is still some difference of opinion concerning that.

End quote. 

For more information, please see the answer to question no.
112075 

Secondly:                       

With regard to giving up sin for fear of what people will say, or because
the individual has no motive to commit that sin, or he refrains from it
because of shyness before people, this has been discussed previously in
detail, in the answer to question number 180814 qv. 

And Allah knows best.