Very interesting find! The actual dogtags Chris Evans wore in the first Captain America movie turned up for auction.
Source.
His dogtags read:
STEVEN G ROGERS
987654320 T42 O
P
The 'O' is his blood type, the 'P' stands for Protestant (so MCU Steve is not a Catholic!). 'T42' indicates he had a tetanus shot in 1942. There is no 'next of kin' or address on the dogtags, so Steve presumably had no permanent residence at the time he enlisted.
Also, this may be an unpopular opinion, but I am so glad CA:TWS jossed the idea of Steve and Bucky growing up in an orphanage together. They tend to be written as co-dependent as it is, it would only have been ten times worse if it was canon they were scrappy little orphans with no one in the world but each other.