Much like lines in some rinks, you will also see logos at center ice.

I have not done this on my rink as of yet, but I might.  What you use for a logo is up to you, what it is made out of is much the same. 

Some are done on a piece of plexiglass and  put down in such a way that it sits a few layers under the top surface.  This is done by placing the logo on the ice and flooding over it until the rink surface is now above the plexiglass.  I have heard that the plexi is subject to heaving and may cause your rink to buldge where the logo is though.

Others use printed logos and paste them with a layer of water to the surface, wait for that to freeze and then resurface several times to get a good layer over the logo.  This is less likely to heave and cause unwanted bumps.

You can also laminate your printed logo and do the same as you would with the previous printed logo.  The plus here is you can reuse this laminated logo year after year.

 These same steps can be done for faceoff dots.

Please keep in mind that anything that has a dark color may, can and probably will cause the ice to melt just like the painted lines.  Unless you can do this on the liner itself and have enough ice above that the darkness isn't an issue.