They are generally referred to as guardian statues. One of the most popular types is guardian lions.
For example, Chinese guardian lions ("Foo Dogs") are well-known and it is mentioned that they share symbolism with Staffordshire dogs:
While Staffordshire dogs originated in 19th-century England, like foo dogs they were used as symbols of protection and status. Staffordshire dogs were often found flanking the fireplace in well-to-do British homes, and were strikingly similar in pose and scale — I can’t help but wonder if they were at all influenced by these ancient guardian statues of China.
The lion statues of the NYC Library are mentioned as guardian lions in the book Public Space by Stephen Carr:
The monumental neoclassic white marble building of the New York Public Library in mid-Manhattan, its forecourt flanked by two reclining "guardian lions" sculpted by Edward C. ...
They are referred to as gate guardians as well:
Statue of a pair of lions often founds in temples in Southeast Asia as the gate guardian. The Balinese winged lion often served as the guardian statue or as the pedestal of wooden column.
Wikipedia / Cultural depictions of lions
Dvarapala (Sanskrit) is a door or gate guardian often portrayed as warrior or fearsome asura giant, usually armed with a weapon, the most common is gadha mace.
Wikipedia / Dvarapala
Gate-guardian sculpture is mentioned in the book "What is stronger than a lion?: leonine image and metaphor in the Hebrew Bible and the ancient Near East" by Brent A. Strawn: