Is it possible to name a term created in a formula? This is the scenario:
Create a toy dataset:
set.seed(67253)
n <- 100
x <- sample(c("A", "B", "C"), size = n, replace = TRUE)
y <- sapply(x, switch, A = 0, B = 2, C = 1) + rnorm(n, 2)
dat <- data.frame(x, y)
head(dat)
#>   x         y
#> 1 B 4.5014474
#> 2 C 4.0252796
#> 3 C 2.4958761
#> 4 C 0.6725571
#> 5 B 4.3364206
#> 6 C 3.9798909

Fit a regression model:
out <- lm(y ~ x, dat)
summary(out)
#> 
#> Call:
#> lm(formula = y ~ x, data = dat)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -2.07296 -0.52161 -0.03713  0.53898  2.12497 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)   2.1138     0.1726  12.244  < 2e-16 ***
#> xB            1.6772     0.2306   7.274 9.04e-11 ***
#> xC            0.5413     0.2350   2.303   0.0234 *  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 0.9297 on 97 degrees of freedom
#> Multiple R-squared:  0.3703, Adjusted R-squared:  0.3573 
#> F-statistic: 28.52 on 2 and 97 DF,  p-value: 1.808e-10

Fit the model again, but use "C" as the reference group:
out2 <- lm(y ~ relevel(factor(x), ref = "C"), dat)
summary(out2)
#> 
#> Call:
#> lm(formula = y ~ relevel(factor(x), ref = "C"), data = dat)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -2.07296 -0.52161 -0.03713  0.53898  2.12497 
#> 
#> Coefficients:
#>                                Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)                      2.6551     0.1594  16.653  < 2e-16 ***
#> relevel(factor(x), ref = "C")A  -0.5413     0.2350  -2.303   0.0234 *  
#> relevel(factor(x), ref = "C")B   1.1359     0.2209   5.143 1.41e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 0.9297 on 97 degrees of freedom
#> Multiple R-squared:  0.3703, Adjusted R-squared:  0.3573 
#> F-statistic: 28.52 on 2 and 97 DF,  p-value: 1.808e-10

The variable, x, was re-leveled in the second call to lm(). This is done in the formula and so the name of this term is relevel(factor(x), ref = "C").
Certainly, we can create the term before calling lm(), e.g.:
dat$x2 <- relevel(factor(x), ref = "C")
out3 <- lm(y ~ x2, dat)
summary(out3)
#> 
#> Call:
#> lm(formula = y ~ x2, data = dat)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -2.07296 -0.52161 -0.03713  0.53898  2.12497 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)   2.6551     0.1594  16.653  < 2e-16 ***
#> x2A          -0.5413     0.2350  -2.303   0.0234 *  
#> x2B           1.1359     0.2209   5.143 1.41e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 0.9297 on 97 degrees of freedom
#> Multiple R-squared:  0.3703, Adjusted R-squared:  0.3573 
#> F-statistic: 28.52 on 2 and 97 DF,  p-value: 1.808e-10

However, can I create a term and name it in the formula? If yes, how?

How to name a term created in the formula when calling `lm()`?
adapted from the info in this comment : Rename model terms in lm object for forecasting
set.seed(67253)
n <- 100
x <- sample(c("A", "B", "C"), size = n, replace = TRUE)
y <- sapply(x, switch, A = 0, B = 2, C = 1) + rnorm(n, 2)
dat <- data.frame(x, y)

out <- lm(y ~ x, dat)
summary(out)

out2 <- lm(y ~ x2, transform(dat,
                             x2=relevel(factor(x), ref = "C")))
summary(out2)

