if one adds mumuskhu to his name, can we assume he has taken diksha

No. Adding the word “mumukshu” (मुमुक्षु) to a name does not mean that a person has taken diksha.

• Meaning: Mumukshu simply means a seeker of liberation (moksha). It indicates a spiritual aspiration and a desire to attain spiritual perfection, and it can apply to both laypersons and monks. It is not a formal vow or initiation.
• Diksha difference: Diksha is the formal initiation into a Jain monastic order (renunciation of worldly life) and is followed by specific vows, adopting a monk or nun’s life, and often a new name that reflects that path (e.g., Muni, Jain Sadhvi, Upadhyaya in some lineages).
• Traditions: There are differences between Digambar and Śvetambar traditions in naming and ordination practices, but in both, “mumukshu” remains a seeker, not a confirmed monk or nun.

If you want to verify whether someone has taken diksha, look for signs of monastic status (renounced life, specific monastic name, attire, and community records) rather than the word “mumukshu” in a name.