I think what the enquirer means to ask is: can P355QH1 be considered P-No. 1 too, like P355NH, seeing that both are P355? The answer is no. First, their chemical composition is not same, not even similar. Two, they are classified under different specifications, one under EN 10028-3, another under EN 10222-4.
Section IX specifies the specification along with the classification, in the table QW-422. One should avoid making the mistake of locating the classification alone. When trying to determine P-number, BOTH the classification as well as specification should be matched.
For example, 16Mo3 grade classified under EN 100216-2 specification is a P-No. 3 metal; while 16Mo3 grade specified under EN 10222-2 and EN 10028-2 is an unassigned metal (confirmed by Sec IX through interpretation IX-23-26).
Seeing another way, this is an interesting question however. Some grades are designated with an optional designator. When one comes across a grade having an optional designator, should it be considered of same P-No. as the original grade? Or not?
Can't think of an appropriate example in base metals right now. But in filler metals - E7018 has a F-no. 4 as per ASME Sec IX. I know that E7018-H4R (H4R is an optional designator indicating restricted diffusible hydrogen and restricted moisture content) is also to be considered as F-no. 4. This however, is not spelt out thus anywhere. Does a similar logic apply to base metals too?