Hi,

Does anyone know the name of this font?

Bodoni Campanile  Suggested by donshottype 
Modern 735  Suggested by donshottype 

Not font, but rather a trademark logo owned by Philip Morris http://trademark.markify.com/trademarks/ctm/l++m+quality+american+blend+l+m/009434754
The base letters, before the inline treatment may be derived from Bodoni Campanile, designed by R.H. Middleton for Ludlow, circa 1930. Vertically extended.
Don

See also the Bitstream version of Bodoni Campanile
Don