Noun and の adjective
むめい
フグは、無名のまま死にたくないと思っている。
Fugu doesn’t want to die in anonymity.
若手のアーティストの中には、無名でも良い作品を作る人がたくさんいます。
Among young artists, there are many unknowns producing good work.
アリアナ・グランデは自分の才能を少しも鼻にかけず、無名の新人歌手にも優しく接するらしいので、とても好感がもてます。
I heard that Ariana Grande is not a bit stuck up in spite of her talent and is very nice to unknown singers too, so I have a good impression of her.
Someone with "nothing" for their name is trying to remain anonymous.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.