The following tables populate dropdowns in a web app.

CREATE TABLE request_types(
    id INT AUTO_INCREMENT PRIMARY KEY,
    name as varchar(32) NOT NULL
);

CREATE TABLE citizenship_types(
    id INT AUTO_INCREMENT PRIMARY KEY,
    name as varchar(32) NOT NULL
);

CREATE TABLE designation_types(
    id INT AUTO_INCREMENT PRIMARY KEY,
    name as varchar(32) NOT NULL
);

The design of all 3 is identical.

When is it better for normalization to put data of these tables into a single one and use another to differentiate what group the values belong to?

Like

CREATE TABLE field_types(
    id INT AUTO_INCREMENT PRIMARY KEY,
    name as varchar(32) NOT NULL,
    category TINYINT NOT NULL
)

CREATE TABLE category_types(
    id INT AUTO_INCREMENT PRIMARY KEY,
    name as varchar(32) NOT NULL
)

with category_types populated like

{
    1:"request",
    2:"citizenship",
    3:"designation"
}