Hmmm, those look cozy. Some of my names are kind of silly, but maybe it will jog someone else's creative juices. I like Primping Cushion.
How about something like
Yorkie Nesty
Show Nesty*
or
Beauty Bar
Beauty Roll
Head Bed
No Mess Head Bed
No Mess Head Rest *
Show Cushion
Primping Cushion*
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