Dear Padma,
No. There is no such requirement on the part of subsidiary company as the section itself is explanatory which is re-produced as under:
25. Power to dispense with “Limited” in name of charitable or other company.—
(1) Where it is proved to the satisfaction of the Central Government that an association—
(a) is about to be formed as a limited company for promoting commerce, art, science, religion, charity or any other useful object, and
(b) intends to apply its profits, if any, or other income in promoting its objects, and to prohibit the payment of any dividend to its members,
the Central Government may by licence, direct that the association may be registered as a company with limited liability, without the addition to its name of the word “Limited” or the words “Private Limited”.
(2) The association may thereupon be registered accordingly; and on registration shall enjoy all the privileges, and (subject to the provisions of this section) be subject to all the obligations, of limited companies.
(3) Where it is proved to the satisfaction of the Central Government—
(a) that the objects of a company registered under this Act as a limited company are restricted to those specified in clause (a) of sub-section (1), and
(b) that by its constitution the company is required to apply its profits, if any, or other income in promoting its objects and is prohibited from paying any dividend to its members,
the Central Government may, by licence, authorise the company by a special resolution to change its name, including or consisting of the omission of the word “Limited” or the words “Private Limited”; and section 23 shall apply to a change of name under this sub-section as it applies to a change of name under section 21.
(4) A firm may be a member of any association or company licensed under this section, but on the dissolution of the firm, its membership of the association or company shall cease.
(5) A licence may be granted by the Central Government under this section on such conditions and subject to such regulations as it thinks fit, and those conditions and regulations shall be binding on the body to which the licence is granted, and where the grant is under sub-section (1), shall, if the Central Government so directs, be inserted in the memorandum, or in the articles, or partly in the one and partly in the other.
1[(6) It shall not be necessary for a body to which a licence is so granted to use the word “Limited” or the words “Private Limited” as any part of its name and unless its articles otherwise provide, such body shall, if the Central Government by general or special order so directs and to the extent specified in the direction, be exempt from such of the provisions of this Act as may be specified therein.]
(7) The licence may at any time be revoked by the Central Government, and upon revocation, the Registrar shall enter the word “Limited” or the words “Private Limited” at the end of the name upon the register of the body to which it was granted; and the body shall cease to enjoy the exemption granted by this section:
Provided that, before a licence is so revoked, the Central Government shall give notice in writing of its intention to the body, and shall afford it an opportunity of being heard in opposition to the revocation.
2[(8) (a) A body in respect of which a licence under this section is in force shall not alter the provisions of its memorandum with respect to its objects except with the previous approval of the Central Government signified in writing.
(b) The Central Government may revoke the licence of such a body if it contravenes the provisions of clause (a).
(c) In according the approval referred to in clause (a), the Central Government may vary the licence by making it subject to such conditions and regulations as that Government thinks fit, in lieu of, or in addition to, the conditions and regulations, if any, to which the licence was formerly subject.
(d) Where the alteration proposed in the provisions of the memorandum of a body under this sub-section is with respect to the objects of the body so far as may be required to enable it to do any of the things specified in clauses (a) to (g) of sub-section (1) of section 17, the provisions of this sub-section shall be in addition to, and not in derogation of, the provisions of that section.]
(9) Upon the revocation of a licence granted under this section to a body the name of which contains the words “Chamber of Commerce”, that body shall, within a period of three months from the date of revocation or such longer period as the Central Government may think fit to allow, change its name to a name which does not contain those words; and—
(a) the notice to be given under the proviso to sub-section (7) to that body shall include a statement of the effect of the foregoing provisions of this sub-section; and
(b) section 23 shall apply to a change of name under this sub-section as it applies it change of name under section 21.
(10) If the body makes default in complying with the requirements of sub-section (9), it shall be punishable with fine which may extend to 3[five thousand rupees] for every day during which the default continues.