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”.