Basically the son has to be called an outcaste(i.e one without any varna) as said by Yogi in comments.
Because the castes are only 4 in number and there is no fifth caste.So one who does not belong to any of the 4 has to be treated as belonging to no caste .Or to be born in a confused caste(that is difficult or impossible to determine).
Manu Smriti 10.4. Brahmana, the Kshatriya, and the Vaisya castes
(varna) are the twice-born ones, but the fourth, the Sudra, has one
birth only; there is no fifth (caste).
When marriages take place between the same castes its easy to determine the caste of the progeny & which is the same as that of the father.
Manu Smriti 10.5. In all castes (varna) those (children) only which
are begotten in the direct order on wedded wives, equal (in caste and
married as) virgins, are to be considered as belonging to the same
caste (as their fathers)
However,in cases where the father is one caste higher than the mother's caste then the son will be called as "anantaras" and he will belong to one caste lower than that of the father.
10.6. Sons, begotten by twice-born man on wives of the next lower castes, they declare to be similar (to their fathers, but) blamed on
account of the fault (inherent) in their mothers
10.14. Those sons of the twice-born, begotten on wives of the next lower castes, who have been enumerated in due order, they call by the
name Anantaras (belonging to the next lower caste), on account of the
blemish (inherent) in their mothers.
Manu Smriti 10.24. By adultery (committed by persons) of (different)
castes, by marriages with women who ought not to be married, and by
the neglect of the duties and occupations (prescribed) to each, are
produced (sons who owe their origin) to a confusion the castes
So,an Ugra is already an outcaste.And on cohabiting with a Kshatriya woman he will create another kind of outcaste or a confused caste progeny.
However,there is this following verse,which says,as far as duties are concerned,an Ugra can be treated as a Sudra also.
10.41. Six sons, begotten (by Aryans) on women of equal and the next lower castes (Anantara), have the duties of twice-born men; but all
those born in consequence of a violation (of the law) are, as regards
their duties, equal to Sudras.
So,treating an Ugra as a Sudra ,the son in question can also be called a Kshattri:
Manu Smriti 10.16. From a Sudra spring in the inverse order (by
females of the higher castes) three base-born (sons, apasada), an
Ayogava, a Kshattri, and a Kandala, the lowest of men
So,basically,the son has to be called an outcaste or a base-born(apasada).And,as far as his duties are concerned he can take upon Sudra's duties.
His prescribed duties are also specified by Manu as follows:
Manu Smriti 10.49. To Kshattris, Ugras, and Pukkasas, catching and
killing (animals) living in holes; to Dhigvanas, working in leather;
to Venas, playing drums