Im not going to address this directly as i do not believe rikuodu is an uzumaki but rather those who hold to the belief that his father is now the uzumaki.
Firstly instead of explaining it, ill identify it.
So far how many shinobi's do we know of who the manga has revealed both their parents.
Hashi/mads/tobi/izuna. The manga only showed their father and not their mother
Kakashi. The manga only showed his father and not the mother
Hiruzen the manga also states his father (sasuke), not the mother.
Ei, his father but not his mother
Now how many shinobi's in the series that the manga hasn't stated either their parents
Kushina we know nothing of either her parents
Minato noth of either his parents
Oro, nothing of either his parents
Jiraiya nothing
Tsunade nothing
Nagato, no name of his parents
Kabuto?.
3rd raikage nothing
Mu, nothing
Out of the akatsuki its only 2-3 people do we know of their parents, the rest nothing.
Out of the hokage's some of the most important characters in the series we either know of one parent or neither.
What i am trying to say is that many, many in fact there is but only a few characters in the series that the manga has identified both their parents. Majority have either parent not being stated or both. Do you know why?
Because they are irrelevant to the story line
Holding to you near the possibility that the sage's father will be an uzumaki is a futile dream. If anything the fact that he has not been mentioned states that he like the other examples i have given of important shinobi's the manga either hasn't stated both their parents of either, shows that he is irrelevant to the story line, he is not important to be drawn on paper or given panel/name.
Next this is if we assume rikuodu had a human father. Its very possible that, after his mother ate the fruit, the seeds might have caused her pregnancy therefore the sage the sage's dad is actually the jubi indirectly, he has many traits of the jubi after all which yes might be connected to his mother eating the fruit, but also i am banking on the fruit causing the pregnancy.
Other thing, its possible that after his mother became a god more or less, anything is possible to her. I wouldn't be surprised that she might have gotten pregnant on her own. Basically using some form of inyouton like what madara did to create zetsu or rikudou used in the form of banbutsu sozo to create the bijuu's. Its not the first time that in a story/myth/religion females have gotten pregnant by their own in some way. Hera the queen of the gods in greek myth gave birth to Hephaestus without zeus.
Finally those who claim it was something similar to minato's scenario with naruto is another futile point. Reason naruto's name wasn't namkizake is because minato had many enemies who will threaten naruto in the future.
Rikudou's mother was a princess, while his father well we know nothing of. But as the princess she might have had enemies. If anything its the fathers name is what would have protected him and not his mothers. Secondly rikudou's mother was basically a god and nothing in the manga states that she died after giving birth to rikuodu, therefore she was alive and looking after her son unlike minato/kushina, therefore there was no need to change his name to protect him when his mother a god was alive. Finally rikuodu is a prince, i would think that he had a fair few bodyguards around him therefore him gaining a name change like naruto would be futile