The reading しもん uses the standard on'yomi for both 諮 (し) and 問 (もん). The 言 (word) radical in 諮 relates to consultation. Wrong readings like しもと use a kun'yomi for 問. しつもん is a different common word. It means to formally ask for advice, opinions, or information from an expert body or individual.

諮 (し) も 問 (もん) も標準的な音読み。専門機関や有識者に意見を求めることを意味します。公式に助言を求める行為です。