If I am reading the magazine "der Spiegel", should I say
(a) Ich lese jetzt der Spiegel.
(b) Ich lese jetzt den Spiegel.
It sounds weird to me to inflect a part of a proper name as in (b).
We do decline names. This will also include an article even if this is part of the name. Sometimes the article will even be omitted when building a contraction with a preposition.
Only rarely the article became an integral part of a name. It is then not separated with a blank. In this case it will not be inflected:
In case we still want or need to include an non-inflected article of a name or a title we should put them in quotes:
Die Produkte heißen Spiegel, Zeit und Stern, nicht Der Spiegel, Die Zeit und Der Stern.