"Blend of Natalie and Lynn"
The name Natalyn is commonly a female name from the "American" origin.
Natalyn is a modern American formation: it takes the name Natalie and replaces its ending with the -lyn suffix familiar from names such as Marilyn and Kaitlyn, so it is best described as a blend of Natalie and Lynn rather than an inherited name with a meaning of its own. The first US birth records for the spelling date from 1959.
The pronunciation of Natalyn is NAT-uh-lin.