How do you pronounce the surname Beauchamp? Do you say "boo champ"?

See https://forvo.com/search/Beauchamp/ for the French and English pronunciation.

Bow shomp 

But you swallow the p.

I do NOT say boo champ! 

Bow pronounced like a bow and arrow, not like the bow of a ship.

it is pronounceed dossunbaribari

Bow-Champ, Bow-Kamp is also another way to pronounce it depending on dialect...

N.Shadows

In the UK we  pronounce it "BEE- cham".

It depends where you are. English speakers mispronounce it differently in every country. 

In France it is bo-shom. The m is hardly pronounced at all. 

It depends on the location.  In the northern US, beech-um, in the south, bo-shahm, with a long o, and shirt a. 

In the UK the English pronunciation given to it is beecham.

Depends on French vs. English pronunciation.

Bow-shom or Bow-sham.  The p is usually silent.

Bow-champ. (like a bow and arrow)