You can consider the following combinations to choose a screen name:
1. Lei Liu*** Dance: Split the surname into "Lei" and "Liu" to express It means two people dancing together.
2. Lei and Liu Tongxin: Splitting the surname into "Lei" and "Liu" expresses the meaning that the two people have the same mind.
3. Lei and Liu accompany each other: Split the surname into "Lei" and "Liu" to express the meaning of the two accompanying each other.
4. Lei and Liu go together: Split the surname into "Lei" and "Liu" to express the meaning of the two moving forward together.
Hope these combinations will be helpful to you.