Possibly. In English people sometimes use "john" to refer to a toilet, but that doesn't mean that those people are named after toilets. And people are named "Rich" even when they don't have any money. His parents might have meant it to imply that their child could be trusted or they could have had many other reasons in mind. And even if they wanted him to be trustworthy when he was born, his life could have taken a completely different route. So even though his name sounds like the word for trust, I would still caution with the Klingon proverb, yIvoq 'ach yI'ol.
In fact, toilets are probably named after a person, Sir John Harrington: http://www.todayifoundout.com/index.php/2010/08/why-the-toilet-is-sometimes-called-a-john/
The Klingon translators for the show had no input into Klingon names, but the writers did have access to TKD, so it's possible. Remember it's not the noun "trust" though, it's the verb, which with no prefix like that could mean "s/he trusts" or "s/he trusts him/her" or "s/he trusts them" or "they trust". The writers wouldn't know that, but you do.