While talking about the possible line of succession, we seem to forget Prince Christophoros, the last born of the children of King George I and Queen Olga. He had a first non dynastic marriage with a rich American lady, (then Princess Anastasia), without kids and then he married an Orleans princess and had Michael the known writer in january 1939.
I found that for his first marriage he was not obliged to give up to his succession rights and his wife was titled Princess of Greece and Denmark
In the years around 1938 Prince Christophoros was married with Princess d'Orleans, highly dynastic marriage, they could reign.
On the 60s his son Michael gave up his rights to wed Marina Carella, so it means he had full rights.
I'm not a specialist in succession laws, but it is true that at this moment, the young Philip was the only young blood, all the others even if before him in line, were elderly, and Prince Michael was born in 1939. Up to January 1939 only Philip was, so it is important the date of this letter.
Furthermore I don't see Princess Alice, considering her previous profile, to expect her son to be the King of Greece. But of course we can't be in people's mind.
Now for the names. It seems that in GRF they never gave middle names with exception made for CP Pavlos names who bear an unusual and unpronounceable number of names, except Maria-Olympia, the boy's names are non practical.
For the previous generations of commun Greek people, the only reason to give more than one name was to honor one of the grandparents, but it is made in a special way. The name is pronounced in the church to make the grandpa happy, but never used after.
For the GRF, King George I kids received of course Greek names, and it was impossible to honor the danish grandparents, as names were very different.
For Queen Olga she honored her father with an historical name for Greeks also.
To cut the story short, now it became a trend to have many names, but then no.