Perfect Rhymes (exact same ending sound):
* There are no perfect rhymes for "Livingston" in standard English.
Near Rhymes (similar but not identical ending sound):
* Slant Rhymes: These are rhymes that share only some sounds, but not all.
* Givingston (this would require a fictional or invented name)
* Livington (a slight variation of the original)
* Giving 'em (this is informal, but technically a slant rhyme)
Eye Rhymes (look alike, but don't sound alike):
* Livingston (this is a bit of a cheat, but technically an eye rhyme)
* Givingston (again, would require a fictional or invented name)
Assonance (shared vowel sound):
* Dividing, surviving, striving
Consonance (shared consonant sound):
* Living, loving, giving
Ultimately, the best rhyme depends on the context and your desired effect.