The laws vary between states but the significance of a commitment ceremony on your relationship status can be researched with the Registrar of Birth Deaths and Marriages in your State.
An interesting quote from Massachusetts Supreme Court Chief Justice Margaret H. Marshall “Marriage is a vital social institution. The exclusive commitment of two individuals to each other nurtures love and mutual support; it brings stability to our society. For those who choose to marry, and for their children, marriage provides an abundance of legal, financial, and social benefits. In return, it imposes weighty legal, financial, and social obligations….Without question, civil marriage enhances the “welfare of the community.” It is a “social institution of the highest importance.”
Because it fulfils yearnings for security, safe haven, and connection that express our common humanity, civil marriage is an esteemed institution, and the decision whether and whom to marry is among life’s momentous acts of self-definition.”