Add name to a mesh

is there a component which lets me give a name to a mesh object?

do you mean emboss or engrave an ID onto a mesh?

Assuming you are referring to the Name attribute of an object, , I believe that technically only exists when the geometry is actually in the active rhino document, (not just GH). So, you could add the name attribute when you bake it into the rhino document.
There is probably something in either elefront or Human, (they both have some great components for adding attributes to objects.)
With that said, I don’t think there are any native components. In a ghpython component, it would be something like this: (Rhino 6)

"""Provides a scripting component.
        B: button to bake the item
        x: meshes to be baked (Set to List Access, type hint MESH)
        y: text input for Name (text from panel)
        a: The a output variable"""

__author__ = "chanley"
__version__ = "2018.10.25"

import Rhino
import sys
import Grasshopper
import scriptcontext as sc
import System

def BakeWithName():
        sc.doc = Rhino.RhinoDoc.ActiveDoc
        for m in x:
            attribs = sc.doc.CreateDefaultAttributes()
            attribs.Name = y
            sc.doc.Objects.Add(m, attribs)
        sc.doc = ghdoc
if B:

I like to use the elefront bake component. However If you need your name to stay in grasshopper before baking and also in rhino after baking, you can add it to the meshes’ UserDictionary. This is not the name attribute that appears in the rhino properties. Every object that inherits from GeometryBase (everything except points and vectors i think) can have an arbitrary dictionary data attached to it.

thanks too all of you!
i have no coding abilities. but elefront is fine for me.