We are not exactly told why Tom denies his mother while he is on his way to be crowned king. However, we can infer his motives by looking at how he feels after he denies her.
Right after Tom denied that he knew his mother, we are told that
a shame fell upon him which consumed his pride to ashes, and withered his stolen royalty. His grandeurs were stricken valueless: they seemed to fall away from him like rotten rags.
If this is what happened to him after he denied her, then we can look at his shame and sadness to give us clues as to why he denied her. After he deines her, his pride is gone and his grandeur seems like it is no longer valuable. This implies that he denied her for the sake of his pride and because he valued the grandeur.
So, in other words, it seems clear that Tom denied her because he liked being royalty. He had come to love being treated like he was so important. Who wouldn't? So now here comes his mother and, if he acknowledges her, this stuff that he's enjoying will be taken away. It's not surprising, then, that he denies her. It's a spur of the moment thing that he does because he doesn't want to go back to being nobody.