The Perrenoud family of La Sagne in the Neuchâtel mountains is one of many which descends from the early settlers of the region, "franc-habergeants" accorded increasing rights and freedom by their overlord, Jean d'Aaberg in the 13th century.  There are actually several distinct families which share the same roots, although their names have evolved differently.

The name Perrenoud comes from a diminutive form of the forename Pierre ("Peter") meaning a rock or stone, from the Greek "petros". 

Brothers Jehan and Jehannin Perrenodz are recorded at Les Glottes near La Sagne in 1463: they were also known as Perrenodz alias Contesse, possibly because of their mother's name.  The descendants of one of Jehannin's sons dropped the first part of the name and became known simply as Comtesse. 

Among Jehan's children were two sons, both called Jean - not uncommon at a time when child mortality was high, and a family wished to perpetuate the father's name.  To distinguish them, the older (or larger) of the two was known as Grand Jean, and his descendants adopted the surname Grandjean-Perrenoud-Comtesse, which is generally shortened to Grandjean today.  As for the second Jean, it would be difficult to recognise his descendants as part of the Perrenoud family, because their surname evolved into Péter-Comtesse. 

Another Perrenoud descendant living at La Sagne in the 16th century was nicknamed Grand Guillaume, and the descendants of this branch became known as Grandguillaume-Perrenoud.  (This surname is generally shortened to Perrenoud today.)

Comtesse

Perrenoud

The alternative spelling Perrenod was common for a time, particularly at Les Ponts-de-Martel, but gradually disappeared.  However, a branch which settled at Couvet adopted the spelling Pernod, and became well-known as distillers of absinthe.  Another branch which emigrated to Prussia in 1710 germanised the spelling of their surname to Pernau, while an emigrant branch in Missouri adopted the spelling Pernoud.

The Perrenoud-André branch are the descendants of Andrey (André) Perrenoud, who was born at La Sagne before 1533.

The Perrenoud-le Favre branch is recorded at Les Ponts-de-Martel from the late 1600s.

A few other suffixes were used briefly, but none survived for long.

Grandjean-Perrenoud-Comtesse

A branch of the family which emigrated to Holland preserved the contemporary spelling of the name, and still uses the form Grandjean-Perrenod-Comtesse.  There is also a French branch of the family, which is known as Grandjean-Perrenoud.   The wider Grandjean-Perrenoud-Comtesse family has a collaborative website and genealogy forum in French (with automatic translation into English).

Grandguillaume-Perrenoud

An Abram Grandguillaume-Perrenoud who lived in Petit Martel in the late 1600s was known as "le Corbe" from a patois word for the local peat marsh.  Some of the next generations were recorded with the surname Grandguillaume-Perrenoud-dit-le-Corbe, but this compound form fell into disuse - doubtless to the relief of their modern-day descendants!