The distinctive function and distinctive character
Trademarks serve to distinguish the goods or services of one company from those of other companies. This is the trademark’s most relevant function for the legal system. Only signs which have the capacity to distinguish, i.e., distinctive capacity, can fulfil that function. For this reason, the rules that regulate trademark law determine that a trademark that does not have distinctive capacity cannot be protected, namely through registration.
In the European Union, both the European Union Trademark Regulation ((EU) 2017/1001) and the Directive approximating the laws of the Member States relating to trademarks ((EU) 2015/2436) include a general rule prohibiting the registration of trademarks "devoid of any distinctive character" (Articles 7(1)(b) of the Regulation and 7(1)(b) of the Directive). Article 7(1)(b) of the Regulation and Article 4(1)(b) of the Directive) and a specific rule prohibiting the registration of descriptive marks, i.e., marks which describe characteristics of the goods or services which they are intended to distinguish (Article 7(1)(c) of the Regulation and Article 4(1)(c) of the Directive).
For abbreviations and acronyms, the prohibition of registration of descriptive trademarks is of particular relevance. This rule has two grounds: first, that only trademarks capable of fulfilling their principal function may be registered, and second, the public interest in preventing the creation of exclusive rights to use terms that other traders may wish to use.
For example, the terms "Orange Juice" cannot be a trademark to identify the product orange juice, not only because they are not able to distinguish the orange juices of one company from those of others, but also because if they were registered, any competitor of the registrant would be prevented from using these terms to indicate the type of product commercialized.
The rule providing for this prohibition has been interpreted by the Court of Justice of the European Union. The CJEU has established that a "sign must be refused for being descriptive if its meaning is immediately perceptible to the relevant public as a sign providing information on the goods and services for which registration is sought." And that the "relationship between the sign and the goods and services must be sufficiently concrete, direct and understood without further consideration." In other words, the method of gauging whether a term is descriptive is as follows: a) identify the meaning of the trademark; b) ascertain whether there is any relationship between the meaning of the trademark and any characteristic of the goods and/or services; and c) if so, ascertain whether the relevant public will identify that relationship concretely and directly and understand it without any further reflection.
The case of abbreviations and acronyms
The question is whether abbreviations or acronyms of descriptive terms should also be considered descriptive. In other words, if the term "ecological" is descriptive to identify ecological products, is its abbreviation "eco" also descriptive? Or if, being the terms "orange juice" descriptive to identify the orange juice product, its acronym "OJ" will also be so. As with any other sign, the answer is given by applying the criterion established by the CJEU.
An abbreviation is descriptive if it is used descriptively and if the relevant public of the product or service in question recognizes the abbreviation as having the same meaning as the full term. In the example of the abbreviation 'eco', to the extent that the public recognizes its meaning as 'ecological', they will see the expression as describing a characteristic of the product or service and not as an indication of the business origin of the product, so 'eco' cannot be registered as a trademark.
Other examples of descriptive abbreviations:
FLEX and FLEXI, as referring to "flexible", to identify footwear (13/06/2014, T-352/12)
MEDI, as referring to "medical", to identify medical services (12/07/2012, T-470/09)
Note that not all abbreviations of descriptive terms are descriptive. It is always necessary to ascertain in the specific case whether the abbreviation is recognized with the same meaning as the full term.
The situation with acronyms is similar. Only if an acronym is understood by the relevant public in a concrete and direct manner and without any further reflection, such as the indication of a characteristic of the product or service in question should it be considered descriptive and consequently be refused its registration. For example, the trademark application TDI was refused for vehicles because the relevant public will understand TDI to mean, respectively, "turbo", "diesel" or "direct" and "injection" (03/12/2003, T-16/02). On the other hand, the acronym OJ, to identify orange juice will not be understood by the relevant public with the meaning of "orange juice", so it will not be descriptive and can be registered.
Differently, in cases where a sign is composed of a non-descriptive acronym in itself, preceding or succeeding a descriptive word combination, it must be gauged whether the "relevant public understands the whole of the sign as a simple expression combined with an abbreviation of that word combination" (E.g., Multi Markets Fund MMF, 15/03/2012, C-90/11 & C-91/11). If so, the application for registration shall be refused.
On the other hand, the trademark will be registered if the relevant public does not rightly and immediately understand the acronym as referring to the combination of descriptive words, but as "a distinctive element that will cause the sign as a whole to prevail over the sum of its individual elements, as demonstrated in the following example: 'The Organic Red Tomato Soup Company - ORTS'." 
 European Union Intellectual Property Office, Guidelines on trade marks and designs, https://guidelines.euipo.europa.eu/1923149/1868526/orientacoes---marcas/2-4-abreviaturas-e-acronimos