How is the name 河内 pronounced, is it コーチ like 講師 = コーシ, or コウチ, like 子牛 = コウシ? I have checked this word in the 三省堂明解アクセント辞典 but cannot find it.
As a name, it is up to the person how they pronounce it. A 戸籍謄本 does not record a reading for a kanji name. Depending on the city hall, most 住民票 now do provide a place to record how a name is to be read. However, that can be changed at will whenever a person desires it. Also, the reading does not have to be a normal reading; it can be nearly anything they wish as long as it is in modern kana. There are no restrictions to which kana readings can be used for any kanji. (The kanji itself, though, cannot be changed without court permission.)
That said, without any special circumstances, 河内 would normally be コーチ. This is an abbreviation of かわうち. The normal phonological development went as follows: kapauti > kaɸauti > kaɸuti > ka[w]uti > kauti > kɔːti > koːti [koːt͡ɕi].