Simply put nearby places allows you to search more vaguely but only return specific results.
In Text Search, if you search for "restaurants", it will search for locations, establishments or names with the text "restaurants".Anything that is related to restaurants.
Meanwhile in nearby search, if you search for "restaurants", it will return restaurant establishments with or without the text "restaurants" but only establishments of "restaurants"
Well, issue is that you are using the wrong parameter.
Check the documentation and you'll see that parameter you should be using is keyword instead of name
It will be then:
https://maps.googleapis.com/maps/api/place/nearbysearch/json?key=[API_KEY]&sensor=false&location=51.52864165,-0.10179430&radius=47022&keyword=%22london%20eye%22
And that's working for me!
EDIT:
As I said, if you try:
https://maps.googleapis.com/maps/api/place/nearbysearch/json?key=[API_KEY]&sensor=false&location=51.52864165,-0.10179430&radius=47022&keyword=%22london%20eye%22&name=%22london%20eye%22
You get as return a lot of results better than using those parameters alone.
UPDATE
As of 2018 the name parameter was deprecated in favor of the keyword parameter, so from now on it is recommended to use only keyword parameter in your requests.
The documentation currently reads
name — A term to be matched against all content that Google has indexed for this place. Equivalent to keyword. The name field is no longer restricted to place names. Values in this field are combined with values in the keyword field and passed as part of the same search string. We recommend using only the keyword parameter for all search terms.
source: https://developers.google.com/places/web-service/search#PlaceSearchRequests
Best Answer
As SKAR said, add %22 when you have spaces. Your search term, instead of Burger King, becomes "Burger King".
URL, as suggested by SKAR:
https://maps.googleapis.com/maps/api/place/nearbysearch/xml?location=-41.21545,174.89416&radius=10000&name=%22strike%20entertainment%20centre%22&sensor=true&key=[YourKey]
Do not replace your %20 (Spaces) by %22, but add them before and after your search term.
Cheers