Unmarried couples living together receive one invitation with both of their names. Luckily, the order is a little flexible here. Specifically, you may choose to put them in alphabetical order or in order of who you know better.
“Mr. Jacob Martin and Ms. Rebecca Wright”
Traditionally, a man’s first and last name are never separated. Always list couples in the order of highest “ranking” if either of them are doctors, judges, military, etc.
“Mr. and Mrs. Phillip Jackson”
“Dr. Elizabeth Jackson and Mr. Phillip Jackson”
“Drs. Elizabeth and Phillip Jackson”
“Dr. Phillip Jackson and Dr. Elizabeth Lewis” (If they have different last names)
“The Honorable Elizabeth Jackson and Mr. Phillip Jackson”
“Reverend and Mrs. Phillip Jackson”
For men who are the second (or third) of their name, write “Mr. and Mrs. Phillip Jackson, junior”. There is a comma and “junior” is written in lowercase letters.
Married or unmarried, same-gender couples with different last names should be listed alphabetically by last name unless one outranks the other.