The rest are deductions based on those sources and on what you've said in your messages.
Rose's son, born 1910 in Akron, OH, was clearly named Ray E. STRAUB.That is the name he's called in the 1920 census living with his grandparents.What's not so clear is whether the father of Rose's son is Ray E. STRAUB (1889-1985), but you started this thread by saying Ray STRAUB's father was Ray STRAUB, and these are the only ones I know of in Akron, OH.You said in another message that Rose had an affair with a married Ray STAUB
but it looks to me like Rose had an affair with a young, unmarried Ray STRAUB.In the 1910 census, Rose STRAUB (age 20) is living with her parents; her marital status is "married," but her husband is not living with her.She doesn't call herself "widowed" or "divorced," so where is her husband?The only Ray STRAUB I know of in Akron is also age 20.He, too, is living with his parents, but he calls himself "single."
Typically, yes, an illegitimate child would bear his mother's surname.But it's also possible for a woman to sue a man for "bastardy" and, if the court rules in her favor, gain the right for her child to bear his father's surname.Also, the father named on a birth certificate is whoever the mother tells the nurse/doctor/midwife is the father.Those in attendance at the birthing are just filling in the certificate based on the word of the mother, so the certificate is not proof of marriage (nor of fatherhood).I have almost no doubt that Ray E. STRAUB, Sr. (1889-1985) is the father of Ray E. STRAUB, Jr. (1910-1985).The name is rare, and that the only two that ever existed were both in Akron, OH, is a coincidence beyone mere chance.But I don't see indisputable evidence that Rose was actually married.
While legally Rose, herself, would not be entitled to use surname STRAUB, that doesn't mean she didn't go ahead and do it to save face.Another possibility is that the marriage was annulled and Ray chose to return to appearing single while Rose, for obvious reasons, chose to appear having been married -- and that may be the most likely scenario.But I was following your lead in assuming Ray (Jr.) was born out of wedlock.
Whatever transpired, it should be in the court records of Summit County, which is where I would be looking ca. 1910.