When I was a kid I had a fear of eating around others too and even in school I would take my food tray to a far off part of the cafeteria and eat my food there instead of at the lunch table.
As far as I know there's no separate term for fear of eating in front of other people it has to due with social anxiety where you have a fear of embarrassment and just a fear of being around people.
I can now eat around other people so my anxiety has improved but it lasted until I was an adult.