Is merely uttering the two declarations of faith sufficient to get rid of the whispers of insulting God and the obscene words that come to mind when mentioning the name of Allah?

The cure for whispers (waswas) is to disregard them, pay no attention to them, and occupy oneself with studying. One should seek refuge in Allah from Satan whenever evil thoughts arise. Furthermore, combating Satan by inviting people to Allah and teaching legal rulings helps in overcoming him. If the thoughts are merely ideas over which you have no control, then Allah has forgiven them as long as you do not act upon them or speak about them, based on the Prophet's (PBUH) saying: "Indeed, Allah has pardoned for my Ummah whatever whispers or thoughts cross their minds, as long as they do not act upon them or speak them." Disliking these thoughts is a sign of strong faith, and the Prophet (PBUH) said concerning them: "That is pure faith." Uttering the testimony of monotheism (Shahada) is good, but it is not obligatory as long as you have not apostatized from your religion.