Design the new hotel with the shape of an egg (8)

I believe the answer is:
innovate
'design the new' is the definition.
I can't tell whether this definition defines the answer.
'hotel with the shape of an egg' is the wordplay.
'hotel' becomes 'inn' (inn is a kind of hotel).
'with' says to put letters next to each other.
'the shape of an egg' becomes 'ovate' (I can't explain this - if you can you should believe this answer much more).
'inn'+'ovate'='INNOVATE'
Can you help me to learn more?
(Other definitions for innovate that I've seen before include "Produce something new" , "Make something new" , "Introduce new ideas" , "Introduce new methods/ideas" , "Introduce changes" .)
