The Republic of Abkhazia has diplomatic missions in Russia, Venezuela, and Syria, all of which recognise the independence of Abkhazia. It also has "representative offices" in other countries, such as Germany, Austria, and Turkey. Those countries do not recognise the independence of Abkhazia. Can they stop Abkhazia from opening such an office? On the one hand, anyone can rent an office as long as the landlord will have them and they are not engaged in criminal activities, but on the other hand: is it really as simple as that in case of unrecognised countries? Could, for example, Germany block such an office from opening or operating?
TLDR: a host country must consent to the existence of any type of diplomatic mission in its territory (this includes the representative offices). This includes countries or regions not officially recognized by the host nation (typically called a De Facto Embassy). If the mission is not recognized then it is, for all intents and purposes, illegal. Notorious examples of illegal diplomatic intervention are resident spies, and undeclared intelligence officers (see also this article).
So, in your example, Germany could indeed block the opening or continued operation of an office spying or lobbying for a foreign power. Someone renting an office with the purpose of doing an undeclared diplomatic mission is an (illegal) Foreign Agent.
The Vienna Convention on Diplomatic Missions and Optional Protocols states:
The establishment of diplomatic relations between States, and of permanent diplomatic missions, takes place by mutual consent.
The sending State must make certain that the agreement of the receiving State has been given for the person it proposes to accredit as head of the mission to that State.
The receiving State is not obliged to give reasons to the sending State for a refusal of agreement.
There are several more articles regarding the rights of the host country expelling diplomats or declare the ambassador as Persona Non Grata.
The most notorious example of a sovereign entity with plenty of diplomatic missions in countries that do not recognize is Taiwan (and this includes a presence in Hong-Kong and Macau). Another that is currently on the news is Northern Cyprus.
In the case of Abkhazia, Germany has showed an interest in brokering relations in the region. As so, it would be nonsensical to forbid the diplomatic operations of Abkhazia in its territory.
For more about the foreign policy of Abkhazia see The foreign policy options of a small unrecognised state: the case of Abkhazia (Frear, 2014).