Probably the most popular alternative is to hyphenate the two names. It's simple and elegant and allows everyone to keep their family name.
Make a Mashup
Have some fun and take parts of your last names and mash them up to create an entirely new name!
Change Your Middle Name
If you really love your last name and want to keep it, you may consider making your given last name your middle name. That will help you stay connected to your past while celebrating your future.
Keep Your Name Professionally
If you are career minded and have earned your success with your current last name you can keep it for your profession. Professionals like relators and doctors do it all the time.
He Takes Her Last Name
Traditionally the female takes the male's last name. It's almost 2017 so it shouldn't be that radical for the male to take the female's name. LGBT couples can negotiate who will change their name, if at all.
Make Something Up
Why not go crazy and just make up a new name for both of you to take? You can even go all out and design a new family crest!
Don't forget doing nothing at all is definitely an option. There is no law that says anyone has to change their name after getting married!