Consistent encoder names (#29492)

This commit updates encoder names to be consistent within documentation
and align with snake casing convention.

docs/plugins/analysis-phonetic.asciidoc

@@ -17,15 +17,15 @@ The `phonetic` token filter takes the following settings:
 `encoder`::
 
     Which phonetic encoder to use.  Accepts `metaphone` (default),
-    `doublemetaphone`, `soundex`, `refinedsoundex`, `caverphone1`,
+    `double_metaphone`, `soundex`, `refined_soundex`, `caverphone1`,
     `caverphone2`, `cologne`, `nysiis`, `koelnerphonetik`, `haasephonetik`,
-    `beidermorse`, `daitch_mokotoff`.
+    `beider_morse`, `daitch_mokotoff`.
 
 `replace`::
 
     Whether or not the original token should be replaced by the phonetic
     token. Accepts `true` (default) and `false`.  Not supported by
-    `beidermorse` encoding.
+    `beider_morse` encoding.
 
 [source,js]
 --------------------------------------------------

plugins/analysis-phonetic/src/test/resources/org/elasticsearch/index/analysis/phonetic-1.yml

@@ -3,7 +3,7 @@ index:
     filter:
       doublemetaphonefilter:
         type: phonetic
-        encoder: doublemetaphone
+        encoder: double_metaphone
       metaphonefilter:
         type: phonetic
         encoder: metaphone
@@ -12,16 +12,16 @@ index:
         encoder: soundex
       refinedsoundexfilter:
         type: phonetic
-        encoder: refinedsoundex
+        encoder: refined_soundex
       caverphonefilter:
         type: phonetic
         encoder: caverphone
       beidermorsefilter:
         type: phonetic
-        encoder: beidermorse
+        encoder: beider_morse
       beidermorsefilterfrench:
         type: phonetic
-        encoder: beidermorse
+        encoder: beider_morse
         languageset : [ "french" ]
       koelnerphonetikfilter:
         type: phonetic