I don't know if ただ信じる is a good song name or not. But I am sure it makes sense and there is no room for misunderstanding. People will take this as "I trust (purely or straightforward without looking around)"). I don't think "ただ信ジル" makes sense as "Trust Jill" in any context but word play, because ”信” alone cannot be a verb and the form must be ”信じる”.

Well what is it you are trying to say ただ信じる is TaDa(Shin)Juru So Believe or Just Believe but people may read it as ただ信ジル which means Like trust Jill [As in Person Jill] it may make sense just would need context too it.