Regarding the statement marked question, for linear regression, if the vector of residuals $e \sim N(0, \sigma^2 I)$ then since $y = X \beta + e$ and $X \beta$ is non-random $y \sim N(X \beta, \sigma^2 I)$ so, yes, $y$ is normally distributed, as well.
Regarding the histogram, normally histograms are made from values that are independent and identically distributed but the observed $y_i$ values under the linear model have different distributions as their means differ so that does not fulfill the requirement for a histogram (except for the trivial linear model consisting of intercept only).
Regarding the statement marked confusion, you might want to look up the Gauss Markov theorem which provides an optimality condition for least squares without the assumption of normality.
Regarding logistic regression, that is not a special case of linear regression.
Logistic regression is an example of a generalized linear model (GLM) and GLMs form a family that is a superset which include both the linear model and logistic regression.
Linear regression (referred to in the subject of the post and above in this answer) refers to regression with a normally distributed response variable. The predictor variables and coefficients are fixed (i.e. non-random) and the residuals are normally distributed as well. In R one uses the
lm function to analyze such models.
Generalized linear regression (GLM) is a superset of linear regression. The assumptions are somewhat similar to linear models but now the dependent variable belongs to an exponential family (not to be confused with the exponential distribution). That family includes the normal, binomial, exponential, poisson and other distributions. The mean of the response variable is related via a link function to a linear function of the independent variables (which is where the linearity comes in). If the dependent variable is normally distributed and the link function is the identity function then GLMs reduce to linear models. If the binomial distribution is assumed then the model is referred to as binomial logistic regression. This can encompass 0/1 data (binary logistic regression). In R one uses the
glm function to analyze GLMs. Note that the general linear model is not the same as the generalized linear model (GLM) so be careful when reading accounts of this.
There are other directions in which one can generalize but normally these are not what one is referring to when one refers to linear regression and these have separate names. For example, one could assume that the $\beta$ values are random (random effects model) or that some are fixed and some are random (mixed effects models). Such models are fit by the lme4 package in R. These are closely related to Bayesian models. Other models include nonlinear regression models where the residuals are still normal and independent but $X \beta$ is replaced with a nonlinear function of $\beta$. The
nls function in R fits such models. Measurement error models ($X$ is random), generalized mixed models (GLMs where coefficients are partly or entirely random), time series models (notably auto-correlation and ARIMA dependence structures among the residuals), multivariate response models ($Y$ is a matrix) and other models may have a form similar to linear regression models as well.
Regarding references, McCullagh and Nelder, Generalized Linear Models (second edition) is useful and has separate chapters for different types of data. For example, Chapter 4 is about binary data.
Another possibility is to find a book with a chapter on GLMs. Here are some at a variety of levels. Chapter 2 of N. Wood, Generalized Additive Models, is about GLMs and discusses both theory as well as examples using R code -- the book as a whole is about GAMs but this chapter is about GLMs. Zuur et al, Mixed Effect Models and Extensions in Ecology with R is a relatively non-mathematical book that discusses GLMs in Chapters 8, 9 and 10 together with R code. McCulloch et al, Generalized, Linear and Mixed Models provides a terse discussion of GLMs in Chapter 5.
Note that a number of those commenting have claimed that $X$ is random. If you do make that assumption then of course the answer would change; however, as you were asking How is Y Normally Distributed in Linear Regression not only is that not the standard assumption but that route will lead to it not being distributed normal whereas the standard assumptions do lead to it being normal so they fulfill the statement of the question as summarized in its subject.
Another interpretation (not mine) is that you are asking about the distribution of the observed values $y_i$ as represented by their histogram. In that case as pointed out in comments under the question it has already been answered here
What if residuals are normally distributed, but y is not? and the question is a duplicate. Again, be aware that that will not lead to the requested explanation of how Y is normal.
EDIT: Have expanded the discussion at the end and added a paragraph on the histogram.
Have moved comments to Note above as comments were getting too long and contentious.