OPTION 1
This a solution that keeps the numbering automatically (following this answer. Nonetheless, I had to suppress the bold face.
---
title: "Untitled"
author: "bttomio"
date: "5/10/2021"
output: html_document
---
```{r, include=F}
library(captioner)
tables <- captioner(prefix = "Πίνακας")
```
```{r tab1, echo=FALSE}
library(kableExtra)
mtcars %>%
kbl(caption=tables("tab1", "Table Caption")) %>%
kable_classic(full_width = F, html_font = "Cambria")%>%
column_spec(1, bold = TRUE, border_right = TRUE, color = "black", background = "lightgrey")
```
```{r tab2, echo=FALSE}
library(kableExtra)
mtcars %>%
kbl(caption=tables("tab2", "Table Caption")) %>%
kable_classic(full_width = F, html_font = "Cambria")%>%
column_spec(1, bold = TRUE, border_right = TRUE, color = "black", background = "lightgrey")
```
-output

OPTION 2
You could try this (fig_caption: no
in your YAML header):
---
title: "Untitled"
author: "bttomio"
date: "5/10/2021"
output:
html_document:
fig_caption: no
---
```{r name, echo=FALSE,results='asis'}
library(kableExtra)
mtcars %>%
kbl(caption = "**_Πίνακας_**") %>%
kable_classic(full_width = F, html_font = "Cambria")%>%
column_spec(1, bold = TRUE, border_right = TRUE, color = "black", background = "lightgrey")
```
-output
