The obvious reason for a character hiding their marital status is because they want to hook up with someone they're not married to. But there are other drivers for keeping this information secret. Perhaps they privately married someone outside their family's faith, culture, or socioeconomic status to avoid being disinherited, excommunicated, or shunned. In some scenarios, a married character may be unable to join an organization or participate in certain activities (usually related to religious orders or governmental and military agencies). And in extreme environments, either party's life may be endangered if the secret is discovered. But a marriage is an intimate and important relationship that's difficult to hide, making this secret a hard one to keep. 

Family and Relationships (primary), Hidden Identity, Illegal or Immoral Acts

HAVING A SECOND FAMILY, HIDING THE TRUTH ABOUT FAMILY

ABANDONMENT, BEING JUDGED, BEING SEPARATED FROM LOVED ONES, BEING UNABLE TO ACHIEVE A DREAM, CONFLICT, CRITICISM, HUMILIATION, LETTING OTHERS DOWN, LOSING THE RESPECT OF OTHERS, PERSECUTION, REJECTION

Feeling hypocritical for being dishonest with people they care about
Not being able to go live out their love publicly
Having to actually deny their feelings about the person they love
Strain in the relationship from having to carefully plan every interaction
Spending a lot of energy leading a double life
The spouse feeling neglected or resentful about the subterfuge
Avoiding family gatherings
Being unable to have a baby
Only being able to spend limited time together\

The character and their spouse claiming to only be roommates