mb_ereg functionality is provided via Oniguruma RegEx library and not via PCRE. mb_regex_encoding() does only support a subset of encoding names, compared to mb_list_encodings() and mb_encoding_aliases().
Currently the following names are supported (case-insensitive):
UCS-4
UCS-4LE
UTF-32
UTF-32BE
UTF-32LE
UTF-16
UTF-16BE
UTF-16LE
UTF-8
utf8
ASCII
US-ASCII
EUC-JP
eucJP
x-euc-jp
SJIS
eucJP-win
SJIS-win
CP932
MS932
Windows-31J
ISO-8859-1
ISO-8859-2
ISO-8859-3
ISO-8859-4
ISO-8859-5
ISO-8859-6
ISO-8859-7
ISO-8859-8
ISO-8859-9
ISO-8859-10
ISO-8859-13
ISO-8859-14
ISO-8859-15
ISO-8859-16
EUC-CN
EUC_CN
eucCN
gb2312
EUC-TW
EUC_TW
eucTW
BIG-5
CN-BIG5
BIG-FIVE
BIGFIVE
EUC-KR
EUC_KR
eucKR
KOI8-R
KOI8R
The list is a mixture of base names and aliases and applies to PHP 5.4.45 (Oniguruma lib v4.7.1), PHP 5.6.31 (v5.9.5), PHP 7.0.22 (v5.9.6) and PHP 7.1.8 (v5.9.6). Be aware of the inconsistency: mb_regex_encoding() accepts for example the base name 'UTF-8' and its only alias 'utf8', but it does not accept aliases 'utf16', 'utf32' or 'latin1'.
Additionally note, that the informal name/alias 'latin9' for ISO/IEC 8859-15:1999 (including the Euro sign on 0xA4) is also not known by mb_list_encodings(). It can only be adressed as 'ISO-8859-15' or 'ISO_8859-15' and for mb_regex_encoding() solely as 'ISO-8859-15'.