Yes, you could take omeprazole in the morning and famotidine at night but there are not many studies investigating this approach. Preliminary results suggest that taking your medication this way may provide superior control of gastric acid secretion at night without compromising the effectiveness of omeprazole in the morning. More research is needed.
One small study that looked at the combination of famotidine and omeprazole as a single pill reported a shortening of the time to reach a more favorable gut ph of >4 and a longer duration of effect. Another study that used Pepcid Complete (a combination formulation that contains famotidine and 2 antacids, calcium carbonate and magnesium hydroxide) reported that omeprazole in the morning and Pepcid Complete at night were superior than omeprazole morning and night.