How to properly filter a BPSK demodulated signal?
You must use a sampling frequency of at least the Nyquist rate, which is greater than 15 kHz in this case. It should be greater than $2(f_c + W/2) = 2 (10~\text{kHz} + W/2)$, being $W$ the signal's bandwidth.

You did not specify the bit rate, which also must be considered to determine the signal's bandwidth, and thus the Nyquist rate.

You signal is probably having time-aliasing. More details in the answers to the following question: A voice signal is band-limited to 3.3 kHz. What is the Nyquist frequency?