i have a monopole antenna with a fixed orientation that's vertically polarized....
I hope I understand the question.
If the signal is vertically polarised and your antenna is also similarly oriented (the dipole is vertical), it will receive at max efficiency.
The same antenna will receive all horizontally polarised signals will 0 efficiency (no reception). And all signals with slanted polarization with reduced efficiency.
Similarly for horizontally polarised signal and horizontal dipole antenna.
An antenna for a circularly polarised signal need two dipoles separated by some distance (depends on the wavelength). A left circularly polarised signal will be received by a corresponding antenna. It will not receive a right circularly polarised signal.
Signals (say one polarised left circularly) can change their polarisation after reflection (left circularly becomes right circularly polarised) and will not be received by the antenna (say designed for the left circularly signal).
So, the answer to your question, is YES.
If your dipole is oriented 45 towards horizontal (and vertical), it will receive both horizontally polarised an vertically polarised signals (but with reduced factors). But you cannot change the polarization of the incident signal.
By the way, if you have a giant reflector and if you can place it wisely, the incident signal can get reflected and change its polarisation. But that is not the question, right?