"pityr"

[cbmvax!uunet!mcnc.org!aurs01!aurw31!waugh (Jack Waugh)]

If your English is typical of the USA, your pronunciation of
"Peter" is probably closer to "pidr" than to "pityr".
A UK Peter would probably come closer to "pita" which of
course is not a name, so it would be typically loglanized
as "pitas".
A two-word name such as "pityr. tames", however, is perfectly
legal.
The "y" has the value of "u" in "butter".  The "r" has that
of the first sound in USA-English "Earl"  ("rl").  Well,
maybe it should be more like a trilled "r" in Loglan, but,
at least, it is the closest letter in Loglan in sound to
that sound in USA English.