Using Commands - GiantLuigi4/StylesPlusPlus GitHub Wiki

/give @p minecraft:name_tag{"display":{"Name":'{"translate":"entity.minecraft.zombie","italic":false,"stylesplusplus:extra_styles":[{"registryName":"stylesplusplus:wavy","globalTime":true,"x":{"scale":3,"speed":1,"startOffset":0,"indexMultiplier":12},"y":{"scale":3,"speed":1,"startOffset":0,"indexMultiplier":12}}]}'}} 1

"stylesplusplus:extra_styles":[{"registryName":"stylesplusplus:wavy"

This defines that the text component uses the wavy text style, the "globalTime":true flag marks that it should use the game tick for animation instead of ticks since the text component was created, and everything following that defines the specific animation seen by this example

All of these properties are defined per style, and are not universal