Zu is a beast as a preposition and its usage can widely vary. Duden lists the definition for the particular usage as follows, in the same category as the usage "zu Hause sein" (at home):
- c) kennzeichnet den Ort, die Lage des Sichbefindens, Sichabspielens von etwas
- (in Namen von Gaststätten) Gasthaus zu den Drei Eichen
My personal interpretation of this usage is a stylized description of the building; "Zur Post" is "by post office" and "Zum Löwen" might merely mean "with lion signage" as knut commented. For a bonus, the "The Prancing Pony" inn in Lord of the Rings was translated as "Zum Tänzelnden Pony" in German.
Found more discussion in another forum at UPenn LDC Language Log - Ask Language Log: German restaurant-name zum? Seems to be an indeed popular question, where no one likely had definitive explanation why zu is used for this purpose, other than it being a tradition or a formulated phrase.
Similar question of usage of zu have appeared in GLSE before. Meaning of "zu" in the name of a Gasthof. My answer above can be interpreted as an elaboration on Ingmar's answer to this. Another example of usage of zu for building albeit a bit different is asked in Wieso heißt es „Universität zu Köln“?. This again is not "(toasting) to", merely describing its location and/or affiliation.