According to PubChem, the IUPAC name of nickel bis(glycinate) is carboxymethylazanide;nickel(2+), which has a given structure of:
![Bis[glycinato(2-)-κ2N,O]nickel](https://i.stack.imgur.com/QzgfI.jpg)
However, according to suggestions in Ref.1, the correct IUPAC name should be bis[glycinato(2-)-$\kappa^2$N,O]nickel.
Since the complex is simply given as $\ce{[Ni(gly)2]}$, it is no need to go for the compllicated name since I consider OP as a nivice to coodination chemistry. Let's look at what we can find in Ref.1. The Ref.1 specifies that:
The number of each entity present has to be specified in order to reflect the composition of the compound. For this purpose multiplicative prefixes (Table 2) are added to the name of each entity. The prefixes are ‘di’, ‘tri’, ‘tetra’, etc., for use with names for simple entities, or ‘bis()’, ‘tris()’, ‘tetrakis()’, etc., for names for most entities which themselves contain multiplicative prefixes or locants. Care must also be taken in situations when use of a simple multiplicative prefix may be misinterpreted, e.g., tris(iodide) must be used for $\ce{3I–}$ rather than triiodide (which is used for $\ce{I3–}$), and bis(phosphate) rather than diphosphate (which is used for $\ce{P2O7^4–}$).
Note: Table 2 in above concept is table of multiplicative prefixes for simple and complicated entities upto 20.
Ref.1 also states that the names of complexes are constructed by adding the names of the ligands before those of the central atoms, using appropriate multiplicative prefixes. Formulii are constructed by adding the symbols or abbreviations of the ligands after the symbols of the central atoms. For xample:

The first structure is relative to OP's question while the second structure is beyond OP's knowledge of the field. The name of the first structure is pentaammineaquocobolt(III) chloride. Note that in complexes, ammonia is named as ammine (with two $m$s) and water is aqua. All other amines would be named ith one $m$ as usual. Also note that five ammonia molecules are named "pentaammine," not "pentakisammine." It is because ammonia is a simple molecule (the molecular formula of this molecule is written as $\ce{Co[(NH3)5H2O]Cl3}$).
On the other hand, if the the ligand has a complex name or multiple bonded metal with more than one ligand or etc., the complex would be named with complicated multiplicative prefixes. For example, look at the second structure of the above image. It is a triply bonded two rhenium atoms with each having four chloride ligands. Thus, it is a bis(tetrachloridorhenate).
According to above example, it is safe to assume that since glycine is simply given as "gly," the name diglycinatonickel(II) is correct. However, if glycine is shown as 2-aminoethanic acid, the the name should be bis[glycinato(2-)-$\kappa^2$N,O]nickel (A $\kappa$-term is required for ligands where more than one coordination mode is possible). Also, note that there is no hypen between bis term and parentesis, technically making the first name given by OP is incorrect! :-)
Note: OP's textbook and what teacher has said are both technically correct.
References:
- Richard M. Hartshorn, Karl-Heinz Hellwich, Andrey Yerin, Ture Damhus, and Alan T. Hutton, "Brief guide to the nomenclature of inorganic chemistry," Pure and Applied Chemistry 2015, 87(9-10), 1039-1049 (DOI: https://doi.org/10.1515/pac-2014-0718).