Is Bernat also a surname?

Yes. Bernat is used as a surname as well as a first name; its surname page has the origin and how many people carry it.

The first name Bernat

A boy’s name from Catalan.

2 syllables Male Also a surname

Catalan origin

Borrowed from Catalan Bernat.

From Wiktionary (CC BY-SA 4.0).

6 on Wikidata, most written-about first

Bernat Martorell
Catalan painter (1390-1452)
Bernat Fenollar
Clergyman, teacher and poet, 1438–1516
Bernard Desclot
Chronicler from the Kingdom of Aragon, 1300–1280
Prince Carlos, Hereditary Duke of Parma
Current head of the House of Bourbon-Parma and a member of the Dutch Royal Family, born 1970
Bernardin Frankopan
Croatian nobleman, diplomat and soldier, 1453–1529
Bernard, Count of Poitiers
French noble, 800–844

What does the name Bernat mean?: Borrowed from Catalan Bernat.
What is the origin of the name Bernat?: Borrowed from Catalan Bernat.
Is Bernat also a surname?: Yes. Bernat is used as a surname as well as a first name; its surname page has the origin and how many people carry it.