Ventura isn't sure as to how long Eaton will be away from the team.
"Just talking to him now, I let him know that he can stay and see this through," Ventura said. "And Robin is a good name. It works either way. Boy or girl. It's pretty universal."
Ventura already has talked to Avisail Garcia, who hit a three-run homer in the White Sox 7-3 win over the Indians on Saturday, about his mistake on the basepaths Friday, when Garcia was picked off first base by catcher Yan Gomes with runners on first and second, one out and the White Sox down 5-0 in the second.
"Talking about down five runs, your run doesn't mean that much," Ventura said. "You can't break up a double play like you used to. So you're playing a little more cautious, base to base, and we need more hits than anything. And we need baserunners. He understands that.
"If he does it again -- it's like anybody else. There will probably be somebody else doing what he was doing. Hopefully, he doesn't do that anymore."