good point of not using a dictonary!
the other points should't be changed:
don't leave out the slicing of 'names' inside format(), as this results in much slower performance for long name lists.
making that if/else shorter degrades readability and performance
same goes for separating the "like(s) this" part

this would be a good approach:
out = ( 0: 'no one likes this',
1: '{} likes this',
2: '{} and {} like this',
3: '{}, {} and {} like this',
4: '{}, {} and {others} others like this'
)
def likes(names):
return out[min(4, len(names))].format(*names[:3], others=len(names)-2)

thabks heeps!

Use http://pythontutor.com/visualize.html see it for youself ;)

Also read this: https://github.com/codewars/codewars.com/wiki/Troubleshooting-your-solution