"利休酒" are the phonetic kanji used for "liqueur."
Lately, there've been a lot of kids with bizarre names using phonetic kanji.
Sometimes kanji are selected solely for their sounds and the meaning is ignored as in 亜米利加 (アメリカ). These are called phonetic kanji.
当て means something like to guess correctly. 字 means letter. So, this is a letter you guessed correctly. This refers to phonetic kanji, which are kanji that are used in words simply for their sounds, not for their meanings. They are there to be phonetic, and that is all. That is why this word refers to phonetic kanji.
The readings are the on'yomi reading for 字 and the kun'yomi reading for 当て. You've seen 当てる in the past, though, so you should be able to read this portion as well. Combine the two together and you have yourself a nice reading.