In our country, people have 2 parts in name ( mostly without adding father's name) and I don't want to add my name to my daughter's name. I would greatly appreciate if could suggest me some last names that meaningfully match with the name "Mashiat". For example, Mashiat Mahnoor.

Here are some meaningful combinations with the name Mashiat:

Mashiat Hamida (a noble and praiseworthy wish)
Mashiat Mubarakah (a blessed wish)
Mashiat Tayyibah (a good wish)
Mashiat Jamilah (a beautiful wish)
Mashiat Hasanah (a good wish)

Mashiat can also be put in front of any Islamic girl name and the meaning becomes "the girl's wish/desire/will/want", as in:
Mashiat Mahnoor (Mahnoor's wish, Mahnoor's ability to make choice, Mahnoor's will power)