According to Japanese 戸籍法 (Family Register Act):
Article 50 (1) For the given name of a child, characters that are simple and in common use shall be used.
(2) The scope of characters that are simple and in common use shall be defined by Ordinance of the Ministry of Justice.
This is the legal basis of maintaining 人名用漢字 list. In other words, 人名用漢字 is a remedial pool for "characters that are simple and in common use" enough to be used in newborn names but not selected in 常用漢字 list. The fact conversely gives 人名用漢字 a certain connotation that it contains those secondly commonest kanji next to 常用漢字 (although 常用漢字 is maintained by MEXT and 人名用漢字 by Ministry of Justice). For example, in 2010, 129 characters were "promoted" into and 5 were "relegated" from 常用漢字.
噌 was introduced in the 2004 expansion, which is largely prepared with a purely frequency-based list, only removing some "obviously unsuitable for name" kanji (糞, 呪, 癌...) in public comments. Thus some kanji hardly has connection to given names. That said, 噌 is originally an onomatopoeic character in Chinese with no intrinsic meaning, which means there is nothing to prohibit you from using it as ateji as much as 味噌 is. A rare surname 一噌 exists as a Noh musician family.