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According to wiki, Manda is name of the wife of Saturn. But in some texts, Manda is used as another name of Saturn.

Which is true among both?

Saturn is known as Manda. It is mentioned at many places as given below:

Next to Brihaspati, come the planet Saturn, the son of the Sun, two lakh Yoyanas higher. He takes thirty months to pass over one Rāśī. This planet causes all sorts of unrest and miseries to all. Therefore He is called a Maṇḍa Graha (a malefic planet). Devi Bhagavat Purana, Book 8, Chapter 16

32. The son of the Sun (Saturn) is always injurious to people; hence it is termed “Manda” (bad); the Moon was attacked with consumption and bears stain on his body (spots in the Moon disc). What to speak of ordinary men? The great men even are subject to the prescribed laws of Fate and Nature. Devi Bhagavat Purana, Book 4, Chapter 20
    

The word Manda as an adjective has several meanings, some of them is bad, wicked, slow, miserable etc.

I mention what is popularly known.

Shani is among 9 planets with a Sloka starting.. Neelanjana Samabhasam etc. Yes, it is the Indian counterpart of the western concept of a concrete planet by that name.

Manda is not another name of another planet. It is an adjective for sluggishness of body /mind in Sanskrit.

The action of Shani is slowness, lethargy, obstacles, a spanner in spokes etc. By praying to Ganesha obstacles are removed.

There are 12 Zodiac signs but Saturn is not among them. A linking shape is imagined connecting celestial bodies or constellations and a name is given (Leo, Virgo etc.) for them.

As a counter-action to his malefic planetary influences Oil is offered in Pooja in his many temples in which icons depict his male form.

The female counterpart Deity is known Jyesta devata.