There's a difference between fate and destiny. Fate is the preordained path of life which happens in-spite of ones speech and action. Destiny is predetermined thing within a person's life that one takes an active course in shaping. In Islam we call it Qada' wal Qadr and both are from Allah.
We cannot control fate. Death is fate, how, when, where we die is unknown. But if we commit suicide, this is destiny under our control.
So yes, we can make du'a and ask Allah for us to be married to a specific person. However, we also must take the steps and try to get married to whomever we like. But the outcome is not in our control. Anything can happen. And whatever happens, we have to understand it was for our best interest, even if we dislike it.
Therefore, make lots of du'a and do your best in pursuing, hoping for the best outcome. Allaho Alim.