I believe you can't search maps because the host chooses it and can change right up until the start of the match, the feature would be kinda pointless if say, you're looking for Cerberus and find a room via search only for it to change to Harpy because they just did Cerberus.
For the most part you can either just ask it chat to switch pact or make a room, rooms fill up quickly and most are pretty friendly to request unless they're farming for something which I have be in the title itself.