In $BF_3$, B is $sp^2$ hybridised and has one vacant p-orbital which gets filled by accepting a lone pair of electron present on the N-atom of $NH_3$. Nitrogen in this adduct acts as donor atom and $BF_3$ acts as an acceptor. So, hybridization of B in $BF_3$ changes from $sp^2$ to $sp^3$ whereas there is no change in hybridization of N in $NH_3$ and in the adduct.