The Corpse Came C.O.D. by Jimmy Starr (J. Coker and Co., 1951)

Found at one of the Lifeline Bookfairs, complete with shabby dust-jacket:

Hector Ross, studio dress designer, disappears following  a tiff with glamorous movie star, Mona Harrison.  A few days later, Ross's body, dumped into a packing case, is delivered C.O.D. to Mona's house.  How her boyfriend Joe Medford, ace crime reporter, sets about the task of finding the murderer, provides a story packed with thrills and suspense.

What do you call a fictional character who likes to name-drop real people's names?

George Burns and Gracie Allen were across the way.  They waved at Mona, who returned the greeting.  Edgar Bergen, without Charlie McCarthy, sat in a corner booth.

(Page 43)

 As I strolled in, I noticed Fred Astaire over in a corner with his producer, David Hempstead.  Carole Landis was at the bar, telling stories of her army tour in Africa... Dorothy Lamour and Paulette Goddard, still in studio make-up, were gabbing about clothes in a far booth.

(Page 113)

I looked around the room.  Janet Gaynor and Adrian, the famous stylist, were sitting in the next booth.

(Page 115)

Jimmy Starr (his real name, evidently!) was a screenwriter and Hollywood gossip columnist in the 1930s and 1940s, so this novel really is a case of "writing what you know".   It was made into a movie starring George Brent and Joan Blondell in 1947.